03-Probability-and-Statistics-Refresher.ipynb

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   "source": [
    "# Probability and Statistics Refresher"
   ]
  },
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     "name": "stdout",
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     "text": [
      "\n"
     ]
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   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='retina'\n",
    "# import libraries\n",
    "import numpy as np\n",
    "import matplotlib as mp\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import slideUtilities as sl\n",
    "from importlib import reload\n",
    "from datetime import datetime\n",
    "from IPython.display import Image\n",
    "from IPython.display import display_html\n",
    "from IPython.display import display\n",
    "from IPython.display import Math\n",
    "from IPython.display import Latex\n",
    "from IPython.display import HTML\n",
    "print('')"
   ]
  },
  {
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   "execution_count": 2,
   "metadata": {
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    "%%html\n",
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   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "Today we'll review the essentials of probability and statistics.  Given the prerequisites for this course, I assume that you learned all of this once.  What I want to do today is bring the material back into your mind fresh."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "## Probability\n",
    "\n",
    "What is probability?  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Historically, the notion of probability has actually been very slippery and hard to pin down exactly.   There are probably at least three ways to view probability in practice:\n",
    "\n",
    "1. as a mathematical exercise involving positive functions that integrate to 1 (i.e., distributions).\n",
    "2. as an encoding of natural rules for reasoning under uncertainty. \n",
    "3. as an idealization of properties of data and processes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For our purposes, we use probability as an abstraction that hides details we don't want to deal with.  This is a time-honored use of probability."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    ">Any simple idea is approximate; as an illustration, consider an object ... what is an object? Philosophers are always \n",
    ">saying, “Well, just take a chair for example.” The moment they say that, you know that they do not know what they are \n",
    ">talking about any more. What is a chair? ... every object is a mixture of a lot of things, so we can deal with it \n",
    "> only as a series of approximations and idealizations.\n",
    "\n",
    ">The trick is the idealizations.\n",
    "\n",
    "Richard Feynman, _The Feynman Lectures on Physics, 12-2_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
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   },
   "source": [
    "Here is an illustration of this principle applied to probability:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
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   "source": [
    ">In a serious work ... an expression such as “this phenomenon is due to chance” constitutes simply, \n",
    ">an elliptic form of speech. ... It really means “everything occurs as if this phenomenon were due to chance,” \n",
    ">or, to be more precise: “To describe, or interpret or formalize this phenomenon, \n",
    ">only probabilistic models have so far given good results.”\n",
    "\n",
    "Georges Matheron, _Estimating and Choosing: An Essay on Probability in Practice_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Probability and Conditioning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
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   },
   "source": [
    "__Definition.__  Consider a set $\\Omega$, referred to as the\n",
    "_sample space._  A _probability\n",
    "  measure_ on $\\Omega$ is a function $P[\\cdot]$ defined on all the subsets of $\\Omega$ (the\n",
    "  _events_) such that:\n",
    "  \n",
    "1. $P[\\Omega] = 1$\n",
    "2. For any event $A \\subset \\Omega$, $P[A] \\geq 0.$\n",
    "3. For any events $A, B \\subset \\Omega$ where $A \\cap B =\n",
    "    \\emptyset$, $P[A \\cup B] = P[A] + P[B]$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Often we want to ask how a probability measure changes if we restrict the sample space to be some subset of $\\Omega$.  \n",
    "\n",
    "This is called __conditioning.__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Definition.__ The _conditional probability_ of an event $A$ given that\n",
    "event $B$ (having positive probability) is known to occur, is \n",
    "\n",
    "$$ P[A|B] = \\frac{P[A \\cap B]}{P[B]}  \\mbox{ where } P[B] > 0 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
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   "source": [
    "The function $P[\\cdot|B]$ is a probability measure over the sample space\n",
    "$B$.  \n",
    "\n",
    "Note that in the expression $P[A|B]$, $A$ is random but $B$ is fixed. \n",
    "\n",
    "Now if $B$ is a proper subset of $\\Omega,$ then $P[B] < 1$.   So $P[\\cdot|B]$ is a rescaling of the quantity $P[A\\cap B]$ so that $P[B|B] = 1.$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The sample space $\\Omega$ may be continuous or discrete, and bounded or unbounded."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Independent Events.__\n",
    "\n",
    "__Definition.__ Two events $A$ and $B$ are __independent__ if $P[A\\cap B] = P[A] \\cdot P[B].$\n",
    "\n",
    "This is exactly the same as saying that $P[A|B] = P[A].$  \n",
    "\n",
    "So we can see that the intuitive notion of independence is that \"if one event occurs, that does not change the probability of the other event.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Random Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We are usually interested in numeric values associated with events.  \n",
    "\n",
    "When a random event has a numeric value we refer to it as a random variable.\n",
    "\n",
    "Notationally, we use CAPITAL LETTERS for random variables and lowercase for non-random quantities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
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   },
   "source": [
    "To collect information about what values of the random variable are more probable than others, we have some more definitions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
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   },
   "source": [
    "__Definition.__ The cumulative distribution function (CDF) F for a random\n",
    " variable $X$ is equal to the probability measure for the event that\n",
    " consists of all possible outcomes with a value of the random variable $X$\n",
    " less than or equal to $x$, that is, $F(x) = P[X \\leq x].$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Example.__  Consider the roll of a single die.  The random variable here is the number of points showing.  What is the CDF?"
   ]
  },
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Jc8TAwEJGR++nsZ6JXVSrz2bPngdaXZakPuaYCUmS5oihoVVUKpsaOrZS2cTQ0KoWVySp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\nEEIIIYQQoi+kTAghhBBCCCH64v8BTMReOoGmwXkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112d0a898>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 270,
       "width": 393
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "plt.figure()\n",
    "for i in range(7):\n",
    "    plt.plot(i,i/6.,'ob')\n",
    "    plt.plot([i,i+1],[i/6.,i/6.],'-b')\n",
    "plt.xlim([-0.5,7])\n",
    "plt.ylim([-0.05,1.1])\n",
    "plt.xlabel('Number of points showing',size=14)\n",
    "plt.ylabel(r'$P[X\\leq x]$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now, consider this CDF of some random variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"b5a0c47c2ab4b68f\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#b5a0c47c2ab4b68f\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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PMT5e1KJKiGFCklpWTU0a2jRiBNx6Kxx2WO6KJKlllOUwJ2DZGOMu8z5Zu6rS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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115a70630>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 274,
       "width": 393
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import norm\n",
    "plt.figure()\n",
    "x = np.linspace(norm.ppf(0.001), norm.ppf(0.999), 100)\n",
    "plt.plot(x, norm.cdf(x),'b-')\n",
    "plt.xlabel('x',size=14)\n",
    "plt.ylabel(r'$P[X\\leq x]$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What does it mean when the slope is steeper for some $x$ values?\n",
    "\n",
    "The slope tells us how likely values are in a particular range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is important enough that we define a function to capture it.  \n",
    "\n",
    "__Definition.__ The _probability density function_ (pdf) is the derivative of the CDF, when that is defined.\n",
    "\n",
    "$$ f(x) = \\frac{dF(x)}{dx}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Often we will go the other way as well:\n",
    "\n",
    "$$ F(x) = \\int_{-\\infty}^{x} f(t)\\; dt $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should be able to see that:\n",
    "\n",
    "$$ \\int_{-\\infty}^{+\\infty} f(x)\\; dx = 1 $$\n",
    "\n",
    "and\n",
    "\n",
    "$$      f(x) \\geq 0 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now, for a discrete random variable, the CDF is not differentiable (because the CDF is a step function).  \n",
    "\n",
    "For the PDF of discrete RVs, we simply plot the probability function of\n",
    "each value.  That is, we plot $P[X = x]$ for the various values of $x$.\n",
    "\n",
    "Another way to think of the PDF is that it consists of impulses at the\n",
    "points of discontinuity of the CDF. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For our example of the single die:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"8d555ce190003448\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#8d555ce190003448\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
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BRwA/Bw6IiMe1VqEkSZI0AMMMDJtN8fHZ0BlB2LKyvPP4zZO001n+3cz8WfeC5mTpLzbf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\n6w+A70TEO1n/CfwTmza2adp4ZWa2Nev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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11728f1d0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 270,
       "width": 390
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "plt.figure()\n",
    "x = np.arange(7)\n",
    "plt.plot(x, 7*[1/6.], 'bo', ms=8)\n",
    "plt.vlines(x, 0, 1/6., colors='b', lw=5, alpha=0.5)\n",
    "plt.xlim([-0.5,6.5])\n",
    "plt.ylim([0,1.1])\n",
    "plt.xlabel('Number of points showing',size=14)\n",
    "plt.ylabel(r'$P[X = x]$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Characterizing Random Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Definition.__ The _expected value_ $E[X]$ of a random\n",
    "variable $X$ is the probability-weighted sum or integral of all possible values of\n",
    "the R.V.  \n",
    "\n",
    "For a discrete random variable, this is:\n",
    "\n",
    "$$ E[K] \\equiv \\sum_{-\\infty}^{+\\infty} k\\; P[K=k] $$\n",
    "\n",
    "and for a continuous random variable with pdf $p():$\n",
    "\n",
    "$$ E[K] \\equiv \\int_{-\\infty}^{+\\infty} k\\; p(k)\\; dk $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The expected value is also called the average or the mean, although we\n",
    "prefer to reserve those terms for empirical statistics (actual\n",
    "measurements, not idealizations like these formulas).\n",
    "\n",
    "The expected value is in some sense the \"center of mass\" of the random\n",
    "variable.   It is often denoted $\\mu$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The mean is usually a quite useful characterization of the random variable.\n",
    "\n",
    "However, be careful: in some cases, the mean may not be very informative, or important.  \n",
    "\n",
    "In some cases a\n",
    "random variable may not ever take on the mean as a possible value.  (Consider again the single die, whose mean is 3.5)\n",
    "\n",
    "In other cases the notion of average isn't useful, as for the person\n",
    "with their head in the oven and feet in the freezer who claims \"on\n",
    "average I feel fine.\" \n",
    "\n",
    "In other words, the mean may not be very informative when\n",
    "observations are highly variable.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In fact, the variability of random quantities is crucially important to characterize.\n",
    "\n",
    "For this we use __variance,__ the mean squared difference of the random variable from its mean.\n",
    "\n",
    "__Definition.__ The variance of a random variable $X$ is\n",
    "\n",
    "$$ Var(X) \\equiv E[(X - E[X])^2]$$.\n",
    "\n",
    "For a discrete R.V. with $E[X] = \\mu$ this would be:\n",
    "$$ Var(X) = \\sum_{x=-\\infty}^{+\\infty} (x-\\mu)^2\\; P[X=x]. $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The units of variance are the square of the units of the mean. \n",
    "\n",
    "To compare variance and mean, we take the square root of the variance.\n",
    "\n",
    "This is called the __standard deviation__ and is denoted $\\sigma$.\n",
    "So variance is denoted $\\sigma^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Next, let's recall the case of the Tesla and Yelp returns from the last lecture:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"59d9024e8ffc6503\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#59d9024e8ffc6503\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1174ae390>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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T5/6yfw15Y0yyMWaAb/35YF/gVPavNsZ0DT5hjDkV5weCEuCrKDyGRJG/Gg+qyIuIiIiA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Hv7W9xX98nXJlJUCXmFws2YC/nfT4mh/Gz22SrxXtmF2ca4u38P/TcaGvvO76OotMim1/H1leo0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\nX4kpNK2qOivdexK2cvIwHTbPwfwiW8CnSue/6+f376Jso7E0dWkgvYTM0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/kHId94CuNj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1178d02b0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 272,
       "width": 377
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "import pandas as pd\n",
    "import pandas_datareader.data as web\n",
    "\n",
    "stocks = ['TSLA', 'YELP']\n",
    "attr = 'Close'\n",
    "data_source = 'yahoo'\n",
    "df = web.DataReader(stocks, \n",
    "                    data_source,                               \n",
    "                    start=datetime(2014, 1, 1), \n",
    "                    end=datetime(2014, 12, 31))[attr]\n",
    "rets = df.pct_change(30)\n",
    "rets.TSLA.plot(label = 'tesla')\n",
    "rets.YELP.plot(label = 'yelp')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Treating these two timeseries as random variables, we are interested in how the vary __together__.\n",
    "\n",
    "This is captured by the concept of __covariance.__\n",
    "\n",
    "__Definition.__ For two random variables $X$ and $Y$, their _covariance_ is defined as:\n",
    "\n",
    "$$\\text{Cov}(X,Y) = E\\left[(X-\\mu_X)(Y-\\mu_Y)\\right]$$\n",
    "\n",
    "Basically, covariance is large when $X$ and $Y$ tend to be both above their means together, and both below their means together."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Low and High Variability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Historically, most sources of random variation that have concerned\n",
    "statisticians are instances of low variability.  \n",
    "\n",
    "The original roots of\n",
    "probability in the study of games of chance, and later in the study of\n",
    "biology and medicine, have mainly studied objects with low variability.\n",
    "\n",
    "(Note that by \"low variability\" I don't mean that such variability is unimportant.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Some examples of random variation in this category are: \n",
    "\n",
    "* the heights of adult humans\n",
    "* the number of trees per unit area in a mature forest\n",
    "* the sum of 10 rolls of a die\n",
    "* the time between emission of subatomic particles from a radioactive material.\n",
    "\n",
    "In each of these cases, there are a range of values that are\n",
    " \"typical,\" and there is a clear threshold above what is typical, that essentially never occurs.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "On the other hand, there are some situations in which variability is\n",
    "quite different.  \n",
    "\n",
    "In these cases, there is no real \"typical\" range of\n",
    "values, and arbitrarily large values can occur with non-negligible\n",
    "frequency.   \n",
    "\n",
    "Some examples in this category are\n",
    "\n",
    "* the distribution of wealth among individuals in society\n",
    "* the sizes of human settlements\n",
    "* the areas burnt in forest fires\n",
    "* the runs of gains and losses in various financial markets over time\n",
    "* and the number of collaborators a scholar has over her lifetime.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "> The banking system (betting against rare events) just lost [more than] 1\n",
    "> Trillion dollars (so far) on a single error, more than was ever earned\n",
    "> in the history of banking.\n",
    "\n",
    "Nassim Nicholas Taleb, September 2008 \n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "![](figs/derivatives-portfolio-variation.png)\n",
    "\n",
    "An example of a run of observations showing high variability.   This figure shows the daily\n",
    "variations in a derivatives portfolio over the timeframe 1988-2008.\n",
    "About 99% of the variation over the 20 years occurs in a single day\n",
    "(the day the European Monetary System collapsed).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Important Random Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Independent Trials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Here is our canonical experiment: flipping a weighted coin.  \n",
    "\n",
    "The coin\n",
    "comes up \"heads\" (aka \"success\") with probability $p$.  \n",
    "\n",
    "We use the standard notation that the corresponding probability (\"tails\", \"failure\") is denoted $q$\n",
    "(i.e., $q = 1-p$).  \n",
    "\n",
    "These are called _Bernoulli trials_; one can think of each trial as a timestep so these are about _discrete\n",
    "  time_.\n",
    "  \n",
    "Notice that by definition, Bernoulli trials are __independent events.__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now we will extend this notion to continuous time.\n",
    "\n",
    "Imagine that you \"speed up\" the coin flipping so that instead of flipping a coin once per second,\n",
    "you flip it $m$ times per second, and you simultaneously decrease the\n",
    "probability of success to $p/m$.   \n",
    "\n",
    "Then you expect the same number of\n",
    "events (successes, heads) per second (i.e., $p$), but events can happen at finer time\n",
    "intervals.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now imagine the limit as $m \\rightarrow \\infty$.  \n",
    "\n",
    "This is a\n",
    "mathematical abstraction in which \n",
    "* an event can happen at _any_ time instant\n",
    "* an event at any time instant is equally likely\n",
    "* and an event at any time instant is independent of any other time instant (it's still a coin with no memory).   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now we can think of events happening at some _rate_ $\\lambda$ that is\n",
    "equal to $p$ per second.  \n",
    "\n",
    "Note that $\\lambda$ has units of inverse time, e.g., sec$^{-1}$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "For each of these two cases (discrete and continuous time) there are two questions we can ask:\n",
    "\n",
    "1. Given that an event has just occured, how long until the next\n",
    "  success?\n",
    "2. In a fixed number of trials or amount of time, how many events\n",
    "  occur?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "These four cases define four commonly-used random variables.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "| | # Trials or Time Until Event | Number of Events in Fixed Time  |\n",
    "|-|:--:|:--:|\n",
    "|__Discrete Trials__| Geometric| Binomial |\n",
    "|__Continuous Rate__| Exponential | Poisson|\n",
    "\n",
    "Each one has an associated distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Geometric Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The geometric distribution answers the question: \"what is the probability there are exactly $k$ trials before the first success?\"\n",
    "\n",
    "Its PDF is given by:\n",
    "\n",
    "$$ P[X = k] = p(1-p)^k. $$ \n",
    "\n",
    "Its mean is $\\mu = \\frac{1-p}{p}$ and its variance is $\\sigma^2 = \\frac{1-p}{p^2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Its pdf looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
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NjpU2J44JkdSRzLw6Iv4KWEwZiPrPEXE6JQR8m9IPeiPlU8C9KGtKvKzhEsPNKHUSZazJ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\nosufBA7lj502Q8gsklJ6PCK2Aksi4u1jVhe9haxv8d35L2q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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1179b05c0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 286,
       "width": 400
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import geom\n",
    "p = 0.3\n",
    "x = np.arange(geom.ppf(0.01, p), geom.ppf(0.995, p))\n",
    "plt.ylim([0,0.4])\n",
    "plt.xlim([-0.5,max(x)])\n",
    "plt.plot(x-1, geom.pmf(x, p), 'bo', ms=8, label='geom pmf')\n",
    "plt.vlines(x-1, 0, geom.pmf(x, p), colors='b', lw=5, alpha=0.5)\n",
    "plt.title('Geometric PDF.  p = 0.3',size=14)\n",
    "plt.xlabel(r'k',size=14)\n",
    "plt.ylabel(r'P[X = k]',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Binomial Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In this experiment there are precisely $N$ coin flips, and $p$ is still\n",
    "the probability of a success.  Now we ask: what is the probability there\n",
    "will be $k$ successes?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For any given sequence of $k$ successes and $N-k$ failures, the probability is $p^k (1-p)^{N-k}$.\n",
    "\n",
    "But there are many different such sequences: $C^N_k$ of them in fact.\n",
    "\n",
    "So this distribution is $P[X=k] = C^N_k p^k (1-p)^{N-k}.$\n",
    "\n",
    "Its mean is $pN$, and its variance is $pqN$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"2f223c49d925bd3e\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#2f223c49d925bd3e\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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z/3KMryEBevn3JEmSpMkXEQBkZozrvF6+UY2ILwMvB96VmZc1bf8H4BTgI5l5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1174bccc0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 286,
       "width": 394
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import binom\n",
    "p = 0.3\n",
    "x = np.arange(binom.ppf(0.01, 10, p), binom.ppf(0.9995, 10, p))\n",
    "plt.ylim([0,0.4])\n",
    "plt.xlim([-0.5,max(x)+0.5])\n",
    "plt.plot(x, binom.pmf(x, 10, p), 'bo', ms=8, label='binom pmf')\n",
    "plt.vlines(x, 0, binom.pmf(x, 10, p), colors='b', lw=5, alpha=0.5)\n",
    "plt.title('Binomial PDF.  p = 0.3, N = 10',size=14)\n",
    "plt.xlabel(r'k',size=14)\n",
    "plt.ylabel(r'P[X = k]',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Exponential Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This random variable is the analog of the geometric in the continuous case,\n",
    "_i.e.,_ the situation in which a success happens at some rate\n",
    "$\\lambda$.  This RV measures the time until a success occurs. \n",
    "\n",
    "Its pdf is:\n",
    "\n",
    "$$ p(x) = \\lambda e^{- \\lambda x}$$\n",
    "\n",
    "The mean is $1/\\lambda$, and the variance is $1/\\lambda^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"9d8d248601fe63f5\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#9d8d248601fe63f5\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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B668fTU1JkiRp/PVzCLmJsgpVuzkfAytatZszMqLMvJ2yd8j6gzYtvKm6f8G1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\n/j+o7r6lSLy5CgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1179909b0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 287,
       "width": 400
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import expon\n",
    "p = 0.3\n",
    "x = np.linspace(expon.ppf(0.01,scale=1/0.3), expon.ppf(0.995,scale=1/0.3), 100)\n",
    "plt.plot(x, expon.pdf(x,scale=1/0.3),'b-', lw=5, alpha=0.6, label='expon pdf')\n",
    "plt.title(r'Exponential PDF.  $\\lambda$ = 0.3',size=14)\n",
    "plt.xlabel(r'x',size=14)\n",
    "plt.ylabel(r'p(x)',size=14)\n",
    "plt.ylim([0,0.4])\n",
    "plt.xlim(xmax=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Poisson Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The Poisson Distribution is the limiting form of binomial, when the\n",
    "number of trials goes to infinity, happening at some rate $\\lambda$.\n",
    "\n",
    "$$ P[k \\mbox{ successes in time } T] = (\\lambda T)^k \\frac{e^{- \\lambda T}}{k!}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "It answers the question: when events happen indepdently at some fixed rate, how many will occur in a given fixed interval?\n",
    "\n",
    "Its mean is $\\lambda T$ and its variance is $\\lambda T$ as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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       "            if (p.length==0) return;\n",
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     "output_type": "display_data"
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    {
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     "output_type": "stream",
     "text": [
      "\n"
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vh+5u5bklSZKkTUE391CsorjprzdGYufyvd4YCyjWmdiZYizGQMQzMkQCn4+Iz1MM1l5U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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aba89e8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 286,
       "width": 394
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import poisson\n",
    "mu = 3\n",
    "x = np.arange(poisson.ppf(0.01, mu), poisson.ppf(0.9995, mu))\n",
    "# plt.ylim([0,1])\n",
    "plt.xlim([-0.5,max(x)+0.5])\n",
    "plt.ylim(ymax=0.4)\n",
    "plt.plot(x, poisson.pmf(x, mu), 'bo', ms=8, label='poisson pmf')\n",
    "plt.vlines(x, 0, poisson.pmf(x, mu), colors='b', lw=5, alpha=0.5)\n",
    "plt.title('Poisson PDF.  $\\lambda T$ = {}'.format(mu),size=14)\n",
    "plt.xlabel(r'k',size=14)\n",
    "plt.ylabel(r'P[X = k]',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The Poisson distribution has an interesting role in our perception of randomness (which you can read more about [here](http://www.empiricalzeal.com/2012/12/21/what-does-randomness-look-like/#more-2450)).    \n",
    "\n",
    "The classic example comes from history.  From the above site:\n",
    "\n",
    ">In 1898 Ladislaus Bortkiewicz, a Russian statistician of Polish descent, was trying to understand why, in some years, \n",
    ">an unusually large number of soldiers in the Prussian army were dying due to horse-kicks. In a single army corp, \n",
    ">there were sometimes 4 such deaths in a single year. Was this just coincidence?\n",
    "\n",
    "To assess whether horse-kicks were random (not following any pattern) Bortkiewicz simply compared the number per year to what would be predicted by the Poisson distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"f878838555d6fa7c\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#f878838555d6fa7c\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Number of Deaths Per Year</th>\n",
       "      <th>Predicted Instances (Poisson)</th>\n",
       "      <th>Observed Instances</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>108.67</td>\n",
       "      <td>109.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>66.29</td>\n",
       "      <td>65.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.0</td>\n",
       "      <td>20.22</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.11</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.63</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.0</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Number of Deaths Per Year  Predicted Instances (Poisson)  \\\n",
       "0                        0.0                         108.67   \n",
       "1                        1.0                          66.29   \n",
       "2                        2.0                          20.22   \n",
       "3                        3.0                           4.11   \n",
       "4                        4.0                           0.63   \n",
       "5                        5.0                           0.08   \n",
       "6                        6.0                           0.01   \n",
       "\n",
       "   Observed Instances  \n",
       "0               109.0  \n",
       "1                65.0  \n",
       "2                22.0  \n",
       "3                 3.0  \n",
       "4                 1.0  \n",
       "5                 0.0  \n",
       "6                 0.0  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "horse_kicks = pd.DataFrame(\n",
    "data = np.array([\n",
    "[0, 108.67, 109],\n",
    "[1, 66.29, 65],\n",
    "[2, 20.22, 22],\n",
    "[3, 4.11, 3],\n",
    "[4, 0.63, 1],\n",
    "[5, 0.08, 0],\n",
    "[6, 0.01, 0]]),\n",
    "columns = [\"Number of Deaths Per Year\",\"Predicted Instances (Poisson)\",\"Observed Instances\"])\n",
    "horse_kicks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"4dc79bf63c1c96e6\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#4dc79bf63c1c96e6\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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YXMX39NNPY9euXejXrx/i4uKQmZkJwzBQu3ZtPPPMM5g6dard8r6+vvjmm2/Q\nu3dvlCtXDmfPnsXRo0dx7Ngxu2YnhmHgnXfewebNm9G7d29UrFgRGRkZ+Oeff1ChQgV07NgR7777\nLpYsWZInpiZNmmDXrl3o3r07oqOjkZGRgbi4OIwfPx7r1q2Dv7+/V/aVJ3XmXiYsLAxffPEFnn76\nadSvXx/R0dFIS0tDSEgI6tWrh4kTJ2LXrl15OjZHRkZi/fr16Ny5M6Kjo3H69GlzO1qVLFkSW7du\nxZAhQ3DjjTdCRBAUFITOnTtj48aN6NOnjxnTlayPI+XKlcP27dsxffp0NG7cGGFhYUhPT0fZsmXR\nunVrfPjhh+YAclYF2ec1a9bEsmXLMGTIENStWxclS5bE+fPnERERgcaNG5v1hYSEuFyP3Bo3boyq\nVavi6NGj5hgTzta/IMdR+/bt8csvv2DQoEGIi4vDxYsXERwcjMaNG2P27Nn46quvnPYRcPR5K1as\nwOjRo3H33XcjNjYW6enp8Pf3R+3atTF69Gjs2bPHbjC+Xr164YMPPkCPHj1Qq1Yt+Pn5mfvngQce\nwMqVK/Hee+/l+ZyoqCh8//33mDJlCu688074+fnh8uXLqFatGp555hns2bMnz37Nz7ZytczixYsh\nIhgwYIDLOoqTWBIPKm4iYrnt4KX9USSd5OK9Wy+PVbpS1u8BjyUiIuCNN97AiBEjMHToUEyfPr24\nw/lPS05ORkxMDEJDQ3H8+PF8jWuS3/9tNsvn++SQdxyIiIiI/oOGDBmCMmXKYM6cOS5HMybvmzZt\nGjIzMzFq1KgCDYZYVJg4/Od4ozk1ERERXWuCgoLw0ksvIT09PU+TOyo6aWlpeOedd1C2bFmvdLou\nTL7FHQARERERFY9BgwYhOTk5330kqPAcOXIEw4YNw1133QV/f//iDscl9nG4ShRdHwdv1J9Td7wX\nqrapl8cqXSn2cSAiousN+zgQEREREdFVhYkDERERERG5xcSBiIiIiIjcYuJARERERERuMXEgIiIi\nIiK3mDgQEREREZFbTByIiIiIiMgtJg5EREREROQWEwciIiIiInKLiQMREREREbnFxIGIiIiIiNxi\n4kBEREWuYsWKMAwDGzduLO5Qrmt9+/aFYRgYP358cYdCRNcBJg5ERDZE5Lp4eVtKSgomTZqEJk2a\nICYmBv7+/ihTpgwaN26MSZMmITk52aPtTN5V0O08d+5cGIYBHx8fL0SV/1jGjRuH3bt3F3coRP95\nvsUdABHruYwXAAAgAElEQVQRXVsWLVqEoUOH4uzZsxARGIaB8PBwnDlzBklJSfjuu+/w+uuv4913\n30XPnj2LO1y6xs2ZMwcbN25EXFwcbr311uIOh+g/jYkDEZEj8cUdQAHFe7f6mTNn4vHHHwcA3Hnn\nnZgwYQJatGgBX19fZGVl4ZtvvsGLL76IH3/8EQ8//DDS0tIwaNAg7wZFRERFgk2ViIjII7t27cKw\nYcMAAA888AC2bNmCVq1awdfXcg3Kx8cHLVu2xJYtW9CxY0eoKp566ik2MSEiuk4wcSAiIo+88MIL\nyMjIQNmyZTF37lyn7d8Nw8CcOXMQExODjIwMvPjiiy7rPXbsGAYOHIjy5csjMDAQlSpVwogRI3Du\n3DmnZZYvX462bduiTJky8PPzQ2RkJGrUqIGHHnoIn376qdNyK1euRMeOHc1+GaVLl8b999+PNWvW\nOFze2ta/RYsWAICFCxeiadOmiIqKgmEYWL58OVq1agXDMDBy5EiX6zl48GAYhoEuXbrkmaeqmD9/\nPlq2bIno6Gj4+/sjNjYWPXr0wA8//OCy3m3btqFDhw6IjIxEaGgobrvtNkyfPh2q6rJcQY0bNw6G\nYaB///4ALNuofv36CAsLQ3h4OFq0aIG1a9c6Lb9792706dMHcXFxCAgIQFhYGCpXrow2bdpg2rRp\nuHTpklmvYRjYsGEDVNXs6G19VapUya7eTZs2YdiwYWjQoAFiY2PN/dumTRssW7bMaTy2Hcizs7Px\n1ltvoXbt2ggODkZkZCQ6dOiAHTt2uNwmFy5cwJQpU3DXXXchMjISgYGBqFy5Mjp27IhFixYhKysr\nT5mC7vMNGzbgwQcfxI033gh/f39ERESgWrVq6NSpE2bNmuUyTqIrJd76w0L5IyIKwGt/6P/tHOeN\n+nPqjvdC1Tb18lilK2X9Hrg6lszvSnwRBOQN8Za3wv6+nDhxAuXLlwcATJo0ye1JsnW5sWPHwjAM\nHD16FGXLljXnxcXF4ejRo5g1axZGjx6NM2fOICQkBJmZmbh06RJUFVWqVMGmTZtQunRpu3rHjh2L\nSZMmmfsqNDQUly9fNk84S5cujcTERLsymZmZ6Nu3LxYtWmSWCwsLM5MTVcWoUaMwadIku3Jz585F\nv3790KxZM9xyyy14++234ePjg/DwcJw7dw5Lly5FcnIy+vfvjxtvvBFHjhxxuC0yMzNRpkwZpKSk\nYMmSJejcubM5Ly0tDZ06dcK6devMzsyhoaFmbCKCadOm4YknnshT78cff4zevXsjOzsbABAREYG0\ntDRkZmaic+fOCAkJwdy5cxEfH4+XXnrJzR7Lu94ikuekd9y4cRg/fjweeeQR+Pj44MMPP4Svry+C\ng4Nx7tw5qCoMw8CSJUvQqVMnu7JffvklOnXqhMzMTACAv78//P397ZLEffv2oVq1avj000/x9NNP\nIzk5GZcvX0ZYWBgCAwPN5cqXL4+tW7cCANLT0xEaGmp3TIiI3f4dPHgwZsyYkWdd+/Xrh3nz5mHs\n2LH44YcfsGbNGvj5+cHf3x9paWlQVQQGBuKbb75B/fr185T/9ddf0a5dOxw5cgQiAl9fX/PYsq7n\noUOHzO8PUPB9PmvWLDz22GPmegYFBUFEkJ6ebi5z8eJF+Pn55d2pdN3y5H+bk+Xz/eQE3nEgIiK3\nrFd9AaBjx44elXnggQcAWP6ZOXvs6nPPPYeSJUti8+bNSE1NRXp6OhISEnDDDTfgzz//xCOPPGK3\n/JEjRzB58mSICMaMGYOkpCScPXsW6enp+Pvvv7F06VK0a9cuz+eMGDECixYtQrVq1bBkyRKkpaUh\nJSUF586dw3vvvYewsDD83//9Hz755BOHcW7fvh3vvvsuJkyYgDNnzuD06dNITk5Go0aN0LlzZwQE\nBOD48ePYtGmTw/Jr1qxBcnIyQkND0b59e7t5vXv3xrp163DHHXdgzZo1uHDhAlJSUpCcnIxXXnkF\nPj4+ePrpp/H999/blTt48CD69++P7Oxs3HfffTh48CDOnDmD1NRUvPHGG0hISEBCQoJXnl6lqkhI\nSMCiRYswc+ZMnDt3DikpKTh48CCaNm2K7OxsPPnkk2ZCYzV06FBkZmaiQ4cO2L9/v7muqamp2Lhx\nIwYNGoSAgAAAQLdu3ZCYmIiGDRsCAKZNm4bExETzZU0aAMtdrq5duyIhIQFnzpzB2bNnkZKSgpSU\nFLzzzjsICQnBrFmznN55UFW888472LFjh3l8pKam4ueff8Ytt9yCS5cumc30bKWkpKB169Y4evQo\nKleujOXLlyM9PR1JSUm4cOECNm/ejH79+pnN+awKss8vXryI5557DiKCAQMG4OjRozh//jzOnTuH\nM2fOYNWqVejZsycMg6d25D08uoiIyK1ff/0VgOUKcfXq1T0qU6NGDfPK5759+/LMV1VkZGTgq6++\nMk8OAaBDhw745JNPoKr4+uuvsWXLFnPeDz/8gOzsbNSoUQMTJkxAqVKlzHmRkZHo1KkTZs+ebfc5\nf/zxB6ZPn47SpUvjm2++QefOnc0r18HBwRg8eDBmzZoFVcWrr77qcF3S09MxevRojB07FmFhYQCA\nkJAQREVFISwsDG3btgVgeeKUI9bpnTt3trsavG7dOixfvhw1a9bEN998g3vuucecHx4ejtGjR2PC\nhAnIysrKczfk1VdfxaVLl1C9enUkJCSgQoUKAICAgAA8/fTTGDduHFJTUx3GUxhSU1Px4Ycf2p3s\nV6hQAYsWLYKfnx9Onjxpt++SkpJw+PBhAMAHH3yAypUrm/NCQkJw11134f3337e7Mu+pwMBAfPLJ\nJ+jQoQMiIiLM6WFhYRgyZAhmzJgBVcV7773ncn1WrFiBLl26mCf6N998Mz766COoKn788UccP37c\nrsykSZNw/PhxREVFYdOmTWjfvr1dn5+GDRvigw8+sLvbVtB9vmfPHqSlpSE4OBgzZ85EbGysOS8i\nIgKtWrXCggUL8iQpRIXpuk4cRKSLiEwXkY0ikioi2SIyz02ZRiLypYicEZELIvKziAwTEafbSkQe\nEZFtInJeRM6KyLcikveSFxHRNco6LkPJkiU9LiMi5vJnzpxxOL9bt26Ii4vLM69Zs2Zo1KgRAGDp\n0qXmdOtJe2pqKi5evOhRHHPnzoWqolu3bnYncLa6dOkCf39/7N27F6dOncoz38fHB88884zTz3jo\noYegqli6dGmepj2XLl3CihUrICJ5Hk87Z84ciAgGDhyIkJAQp3UDwLfffmvXFOHzzz+HiGD48OEO\nm6YMGzYMQUFBTmO+UuXLl0ePHj3yTI+JiUG9evUAWE52rUJCQsyr4bmbknmb9S7U1q1bnTbnaNy4\nsV0Ca1W3bl2UK1cOgP36AMD8+fMhIhgxYgTKlCnjUSwF3efWY//y5csOv09EReG6ThwAvADgCQC1\nARyHmwb+ItIRwAYAdwP4DMDbAEoAmApgsZMyUwB8BKAMgFkA5gO4GcBKEXm8UNaCiOg61axZM6fz\nmjZtClXFzp07zWn169dHqVKlzCYss2fPNq9iO2Nt7mHtsO3oVa5cOVy+fBmApbN2blWqVLG7u5Fb\nu3btEBYWhuTkZKxevdpu3ooVK5CWlobo6Gjce++9DmObMGGC09juvPNOAJYOuNYTxoMHD+Ls2bMA\ngCZNmjiMKTg4GLfffrvLbXMl7rjjDqfzrFfDU1JSzGmBgYHmPm3VqhVeffVV/Pzzz3maMxVUVlYW\nPvzwQ7Rp0wZly5ZFQECA2ZHauu8uXbpkF5OViJjb2dP1OXLkiJlktmnTxuM4C7rPq1atiqpVq+Kf\nf/5BgwYN8NZbb+H333/3+HOJCsP1njg8DaCaqoYDeBxmL968RCQUwGwAmQCaquogVR0FoA6A7wE8\nKCLdcpVpCGA4gAMAblHVZ1X1SQC3A0gGMEVE8n/PlYjoKmM98XJ00uWMqprLOzvptm1u4WxeUlKS\nOS0iIgLz589HqVKl8Msvv2Dw4MGoVKkSypYti759+zrsS3Hy5EmICNLS0vD33387fakqRAQXLlzI\nU8cNN9zgcl39/f3RuXNnqCoWL7a/zmTtkN29e/c8/Q1OnjwJwHIHxVVs1g601thst4mzuyi229Ab\nQkNDnc6zNl2yJmNWH3zwAWrVqoWkpCS8+OKLuO222xAREYH27dtj4cKFDp8+5In09HQ0adIEgwYN\nwpo1a3Dq1Cn4+voiOjoaZcqUsbsbYNuR+ErWx/bOVH6aVxV0nxuGgUWLFqFcuXI4dOgQhg8fjpo1\nayIqKgrdunXDypUrPY6BqKCu68RBVTeo6p8eLt4VQBSAxaq6y6aODFjuXAiAIbnKDIHlLsarqnrO\npsxRAO8C8AfQr+BrQER0dahZsyYA4J9//vH4Kudvv/2GjIwMAECtWrUKLZY2bdrg0KFDmDVrFrp3\n747Y2FicOnUK8+bNQ7NmzfDYY4/ZLW+9oj116lRkZWW5fGVmZjq8gu/s0bO2rM1Lli9fbj7hKTU1\nFV999RUAOBxF2xpbQkKCR7EVpP3/1SQuLg67d+/G559/jsGDB6NWrVpIT0/HqlWr0Lt3b9SvX99h\n4ubO+PHj8f333+OGG27AvHnzcOrUKaSlpeGvv/5CYmKiXd+E4n5C35Xs89tvvx0HDhzAggUL8Mgj\nj6By5cpISUnBsmXL0LFjR7Rv377Y14+ub9d14pBPzWFJAlY7mLcRwAUAjUSkRK4ycFJmFSzJRovC\nDJKIqDg0a9bMvFqekJDgUZnPP/8cgKUZiLPmNK7aulvnObraHxoaigEDBmDx4sU4duwY9u7di0cf\nfRQAMHv2bKxatcpc1vo416NHj3oUd0G1aNECZcqUQXp6OlasWAEAWLZsGTIyMhAXF+fwUZ7W2Jw9\nxtUZ223iyTa8mhiGgfvvvx8zZszAnj17cPLkSbz++usIDAzErl27MG7cuHzXuXTpUogI3nnnHfTq\n1QtRUVF28x31W7lSto8Jzs/+K+g+t/L390fPnj3x0Ucf4cCBAzh48CBGjx4NEcGqVavw/vvvF6he\nIk8wcfiX9TEh+3PPUNUsAIcA+AKoBAAiEgQgFkCaqjr6i3Qg571a4YdKRFS0YmNj0aZNG/OxlWlp\naS6XP3/+PN59912ICNq1a+e0Oc2GDRuc1rFhwwaICOrWres2vho1auD9999HgwYN8tTbsGFDqKp5\n5d9bDMNAt27doKrmU5QWL14METHvRuRmjc020fFEpUqVzKcHOXvU7YULF7B9+/Z81VscoqOjMXz4\ncAwbNgyqmueYsHaodnUl3XpHoU6dOg7nf/3114UU7b8qVKhgNoH68ssvPS5X0H3uKo5XXnkF3bt3\nB+D6O0V0pZg4/Cs8593Zs+us063Pecvv8kRE17Tx48ejRIkSSExMRJ8+fczBrXLLyspCnz59cPLk\nSZQoUcLpFWRVxSeffOKwc/PGjRvx3XffAQC6du1qTs/dZj4362NW//nnH3Nanz59ICLYt29fnke1\n5mbtcFxQ1gRh9erV+O2337B+/XoAjpspAZZRi63LOxu92llsXbp0garirbfecrhdpk2bVqBmP97i\n7HixcrTvgH+fJuRq34SHW/4l//LLL3nmpaenY+LEifmK1VO9e/eGquKNN94w+y64U9B97smxr6p5\nth9RYWLiQEREHqlbty6mTp0KwNJcqVGjRli9erV5QpiVlYU1a9agUaNGWL58uTn6rbOrwCICPz8/\ntG7d2nzSjKpi5cqV6Nq1K0QErVq1sntE5owZM9C6dWssXrwYf/31lzk9NTUVEydONE/U77vvPnNe\nzZo1MXz4cKgqhgwZgjFjxuDEiRPm/PPnz5uDZ9kmKQVRr149VK5cGRkZGXj44YeRlZWFW2+91ewj\nktt9992Hzp07Izs7Gw888ACmTJmC06dPm/PPnDmDpUuXon379nj22Wftyo4ePRoBAQHYt28fOnbs\naCZgly5dwltvvYWXXnrJbkyD4rZ3717cfPPNmDZtGg4cOGBOz8zMxLJly/Dmm29CRNC6dWu7cjfd\ndBNUFZ999pndCNO2WrZsCVXF8OHD7e7A/Pjjj2jRooX5OOHCNmrUKMTGxiIpKQl33303Vq5caZ7g\nZ2ZmYsOGDejZs6ddk7GC7vMvv/wSjRo1wgcffGDX7O7ixYuYPXs2Fi5c6HD7ERUmjhLyL+sdgnAn\n863Trel/fpf3iKsRPl9++WXEx8fnpzoiokL1+OOPIzw8HE8++SR27NiBNm3awDAMREREIDU1FVlZ\nWRARhIeH491333XaRMdqypQpGDNmDO666y6EhIQgKysLFy9ehIigatWqmDNnjt3yqoo1a9aYV2qD\ng4NRokQJ88qsiGDw4MF5Tp4mT56MixcvYsaMGXjttdfw2muvISwsDCKCc+fOmU9Uat68Oa5Uz549\n8corr2Dnzp0QEfTq1cvl8vPmzTNHYh45ciRGjRqF8PBwZGZmmk3CRAT9+tk/a6NSpUr46KOP0Lt3\nb6xevdpsvpSWloasrCx06dIFQUFBmDfP5fBFXuOoadGvv/6KZ555Bs888wz8/f0RHByMs2fPIjs7\n23wk6tixY+3K9O7dG1OmTMHmzZsRFRWF6OholChRAuXKlTNH6n7llVewdu1aHDt2DM2aNUNAQAB8\nfHyQnp6O4OBgfP7552jVqlW+YvVEqVKlsGrVKrRr1w6HDx9Gx44dUaJECYSFhSE1NRWZmZkQEUye\nPNmuXEH3+datW80RswMDAxEQEICzZ8+ax2+7du0waNCgAq0LXV/i4+ML1F/IHSYO//odlseoVgOw\ny3aGiPgAiIPlUa0HAUBVL4jICQBlRaS0g34OVXPe8/SZcIVPQyC6SsQXdwBXr169eqFt27aYOXMm\nvvzyS+zfvx9nz55FZGQkqlatirZt22Lw4MEuxz0ALCdGVapUwfbt2zFu3DisXr0aSUlJiIuLw4MP\nPogXXnghzyMye/XqhdDQUKxduxa7d+/GyZMnkZaWhrJly6JevXoYOHCgOYqzLcMwzI6z77//PjZt\n2mTesahQoQJq166N++67z2wnnjtOVxd1cnvooYfMEagNw3A4SJqtoKAgLFu2DKtWrcL//vc/bNu2\nDUlJSTAMA1WrVkXdunXRtm1bdOnSJU/Z7t27o1KlSpgwYQK+++47ZGRk4KabbsKAAQMwdOhQ9OvX\nL1+x23K13p5sk9zza9asiWXLlmHt2rXYtm0bEhMTcebMGUREROCmm25Cjx49MGjQoDwjH1evXh1r\n167FpEmT8OOPP+LUqVPIzs42+z4Alqc1/fDDD3jppZewZs0apKSkICoqCp07d8bo0aNRo0YNhzE5\nizU/br75Zuzduxdvv/02EhISsH//fly4cAEVKlTArbfeih49epgDyFkVZJ/fc889WLBgAdauXYud\nO3ciMTERqampiIqKwm233YY+ffq4TdTpvyM+Pt7pxeYrOd7lv3KiKiJNAXwLYIGq9nEwvx+ADwHM\nVdV+uea1ALAWwHpVbWEzfS6AhwH0V9W5ucqMh+UxrvGqOt6D+BTwXuLw70Hijfpz6o73QtU29f5X\njlXyHuv3wNWxdCV/UK8m/L4QEf03ePK/zcny+f6Hxz4O/1oK4DSAHiJiDrUpIv4AXoHljHtGrjLv\nw3LWPFZEImzKVIRlxOpLAOZ4M2giKlyqel28iIiICtt13VRJRDoCeCDnV+uwkY1E5KOcn0+r6ggA\nUNXzIjIIwBIA60XkY1hGf74fluZLS1R1iW39qvq9iLwJ4BkAu0VkKQA/AN1heZrS0JzB4IiIiIiI\nrmnXdeIAoA4A22ZJCktfhbic3w8DGGHOVF2e06RpLIDOAAIA/AFLYvC2ow9Q1edEZDcsdxgGAcgG\nsAPA66paOA9pJiIiIiIqZv+ZPg5XO/ZxcCGnXh6rdKXy2w6UiIjoasc+DkREREREdFVh4kBERERE\nRG4xcSAiIiIiIreYOBARERERkVtMHIiIiIiIyC0mDkRERERE5BYTByIiIiIicouJAxERERERucXE\ngYiIiIiI3PIt7gCIiIravyOpExERkad4x4GIiIiIiNziHQci+s9Q1eIOgYiI6JrFOw5EREREROQW\nEwciIiIiInKLiQMREREREbnFxIGIiIiIiNxi4kBERERERG4xcSAiIiIiIreYOBARERERkVtMHIiI\niIiIyC0mDkRERERE5BYTByIiIiIicouJAxERERERucXEgYiIiIiI3GLiQEREREREbjFxICIiIiIi\nt5g4EBERERGRW0wciIiIiIjILSYORERERETkFhMHIiIiIiJyi4kDERERERG5xcSBiIiIiIjcYuJA\nRERERERuMXEgIiIiIiK3mDgQEREREZFbTByIiIiIiMgtJg5EREREROQWEwciIiIiInKLiQMRERER\nEbnFxIGIiIiIiNxi4kBERERERG4xcSAiIiIiIreYOBARERERkVtMHIiIiIiIyC0mDkRERERE5BYT\nByIiIiIicouJAxERERERucXEgYiIiIiI3GLiQEREREREbjFxICIiIiIit5g4EBERERGRW0wciIiI\niIjILSYORERERETkFhMHIiIiIiJyi4kDERERERG5xcSBiIiIiIjcYuJARERERERuMXEgIiIiIiK3\nmDgQEREREZFbTBwcEJF2IrJGRI6JyAUR+VNEPhWRBk6WbyQiX4rImZzlfxaRYSLC7UtERERE1wWe\n2OYiIpMBrARQB8AqAG8B2AHgfgDfichDuZbvCGADgLsBfAbgbQAlAEwFsLjoIiciIiIi8h5R1eKO\n4aohIqUBnADwN4BbVPWMzbymAL4FcFBVq+RMCwXwJ4BQAI1UdVfOdL+cZRsA6Kmqn3rw2QoA3tof\nIpLzkzfqz6k73gtV29TLY5WIiIjoyljPCVVV3CyaB+842KsAyzbZZps0AICqbgBwHsANNpO7AogC\nsNiaNOQsmwHgBVjOqId4O2giIiIiIm9j4mDvAIAMAPVEJNJ2hog0geXOwtc2k5vDcgl/tYO6NgK4\nAKCRiJTwTrhEREREREXDt7gDuJqoaoqIjATwJoBfRSQBwBkAVQB0gCVBeMymSPWc9/0O6soSkUMA\nagGoBOB3b8ZORERERORNTBxyUdXpInIEwP8ADLSZ9QeAuap62mZaeM57qpPqrNMjCjdKIiIiIqKi\nxaZKueTccVgKS+JQGUAwgNsBHAKwSEReK8bwiIiIiIiKBRMHGzlPTnoNQIKqjlDVw6p6SVV/AtAJ\nlicuPSsiFXOKWO8ohOepzH762XzE4PQVHx+f31UiIiIiov+Y+Ph4p+eTV4KJg732sHR2Xp97hqpe\nBPADLNvstpzJ1n4L1XIvLyI+AOIAZAI46GkAqur0xcSBiIiIiNyJj493ej55JZg42PPPeb/ByXzr\n9Iyc929geeRqawfLNgUQBOA7Vb1caBESERERERUDJg72NsGSCDwqImVtZ4hIGwB3AbgEYEvO5KUA\nTgPoISK32yzrD+AVWO5ezCiCuImIiIiIvIpPVbK3FJZxGu4FsE9EPgfwFyyPVG2Xs8woVU0BAFU9\nLyKDACwBsF5EPgaQDOB+WJovLVHVJUW8DkREREREhY6Jgw1VVRFpC+AJAD0APABLc6NkAP8PwHRV\nXZerzPKcTtVjAXQGEADLo1ufAfB2EYZPREREROQ1cqWdJKhwiIgCuOJOKy7qz/nJG/Xn1B3vhapt\n6uWxSkRERHRlrOeEqprvRyyxjwMREREREbnFxIGIiIiIiNxi4kBERERERG4xcSAiIiIiIreYOBAR\nERERkVtMHIiIiIiIyC0mDkRERERE5BYTByIiIiIicouJAxERERERucXEgYiIiIiI3GLiQERERERE\nbjFxICIiIiIit5g4EBERERGRW0wciIiIiIjILSYORERERETkFhMHIiIiIiJyi4kDERERERG5xcSB\niIiIiIjcYuJARERERERuMXEgIiIiIiK3mDgQEREREZFbTByIiIiIiMgtJg5EREREROQWEwciIiIi\nInKLiQMREREREbnFxIGIiIiIiNxi4kBERERERG4xcSAiIiIiIreYOBARERERkVtMHIiIiIiIyC1f\nb1QqIn1yfkxQ1XMelgkB0BkAVHWeN+IiIiIiIqKC8UriAGAOAAWwHcCvHpYpnVMuGwATByIiIiKi\nq8jV2FRJijsAIiIiIiKydzUlDj4575nFGgUREREREeVxNSUO1XPek4s1CiIiIiIiyqNQ+jiISBMn\ns+4UkSg3xf0BVAbwHCz9In4qjJiIiIiIiKjwFFbn6PWwnPTbEgD/y0cdklPHzEKKiYiIiIiICklh\nNlUSm5ejae5exwE8oaoJhRgTEREREREVgsK649Dc5mcB8A0sdw8GADjkopwCuATgpKoeK6RYiIiI\niIiokBVK4qCqG2x/FzFvOvygqp6O40BERERERFcpbw0AF5fzfsJL9RMRERERURHySuKgqke8US8R\nERERERWPq2kcByIiIiIiukp5q6kSAEBEfAC0BdAUQCUAofh3hGhnVFXv8WZcREXJps+PV6nmfiIy\nERERUeHxWuIgIvUBLIAlYTAnuyii+HcsByIiIiIiuop4JXEQkcoA1gAIgSUZuAxgP4BkANne+Eyi\nq5+3cuKiuaNBRERE/23euuMwFpZmSdkA4gG8parnvfRZRERERETkZd5KHO6F5fLqu6o6wUufQURE\nRERERcRbiUN0zvtSL9VPRLl4uxM2O18TERH9t3nrcaxnct7TvVQ/EREREREVIW/dcfgRQAcA1QHs\n9NJnEJGt+GusXiIiIrqmeOuOw9uwPOrlMS/VT0RERERERcgriYOqrgPwGoDGIjJbRPy88TlERERE\nRFQ0vDWOQx8AvwHYAqA/gLYishTAPgAX3JVX1XneiIuIiIiIiArGW30c5sB+tKsyAIZ6WFYBMHEg\nIiIiIrqKeCtxADicLRERERHRdcNbiUOcl+olIiIiIqJi4JXEQVWPeKNeIiIiIiIqHt56HCsRERER\nEZ1fQhYAACAASURBVF1HmDgQEREREZFbTBycEJF7RORzETkpIpdE5ISIfCUirR0s20hEvhSRMyJy\nQUR+FpFhIsLtS0RERETXBW+N43DwCoqrqlYutGAKQET+D8BzAI4BWA7gNIAbANwOoBmAr2yW7Qhg\nKYCLAD4BkAygA4CpABoB6F6EoRMREREReYW3nqpUMR/LKuwf3arOFiwKIjIIlqThIwCDVTUz13wf\nm59DAcwGkAmgqaruypn+IoBvATwoIt1U9dOiip+IiIiIyBu8lTjM9WCZYAA1ANwMS7KwE8AeL8Xj\nERHxA/AKgCNwkDQAgKpm2fzaFUAUgDnWpCFnmQwReQHAOgBDADBxICIiIqJrmrcex9rP02VF5FZY\nru7XBPCKqi73RkweaglLk6Q3AaiItANwE4BLAH5Q1a25lm8OS9Kz2kFdGwFcANBIREqo6mXvhU1E\nRERE5F3/v737DpOlLBM2fj8ECYIgIEFECQoGQJIooCQREQkuguy3BhQBEwq4uioiDIqLGJYgLriC\nCpgIYkYQJUlSiQouQYIEEQQOcABJ5zzfH2/1Tp8+3V0TOsyZc/+uq66e6Xqr+unqmp566k39nDl6\nTDLzjxGxNXANcEpEbJiZNw8pnFdREoGngKsZrQ0BiIi4CNg1M++vnlurerypdUeZOSsibgNeDqwO\n3NjPwCVJkqR+mhKj/mTmw5TOxEtQ+hcMy/KU/hYfB2YDmwFLAutSahU2Z85mR0tVjw932F/j+aV7\nHqkkSZI0QFMicaj8rnrcdogxNI7H08COmXlZZj6emdcDuwB3AVtExKuHFqEkSZI0BFMpcWh0Ol5x\niDE8VD1enZl3Nq/IzH8y2pdh4+qxUaOwFO01nn+ow/q5RETHZWRkZKy7kSRJ0nxqZGSk4/XkZEyl\nxGHz6nHmEGNo9EPodKE/o3pcrKX8mq0Fq2FbV6MM1TrmeS0ys+Ni4iBJkqQ6IyMjHa8nJ2NKJA4R\n8VrgM5SOyL+rKd5Pv6lieHmH9WtXj7dVj+dR+kTMNZs0sAWwOHCJIypJkiRpXtevmaMPHkOxBYDn\nUkYyejXlAjwpQ6EORWbeERE/A3aMiP0z86jGuojYFngjpdahMXP0GcARwL9GxLGZeWVVdhHKfBAJ\nHDfI9yBJkiT1Q7+GYx1hfDNAB6VD8r9n5vl9iWjsPgSsB3ylmsfhaspwqjtTmh3tlZkzATJzZjXT\n9OnABRHxA+BBYCdK86XTM/P0IbwHSZIkqaf6OY9DXe+LpPRnuBW4EPh6Zt7Qx3jGJDPvjogNgYMp\nCcDrgEeAnwBfyMwrWsr/JCK2AD5NGXlpUeAvwAHAVwcZuyRJktQv/Zo5ekr0nZiozHwA2K9axlL+\nMmCHvgYlSZIkDdE8fYEvSZIkaTBMHCRJkiTV6mcfh7lExLOBZapfH8zMxwb5+pIkSZImpu81DhGx\nbkR8PSJupXQyvr1aHomIWyPi+IhYt99xSJIkSZq4viYOEfEF4EpgL2BVykhLzcuqwN7AVRFxeD9j\nkSRJkjRxfWuqFBFHA/syOizrDcDlwN+r31ekTPz2sqrMf0TEYpm5f79ikiRJkjQx/Zo5ehPgw5S5\nGm4A9snMizuU3Qz4OvBy4MMR8YPMvLwfcUmSJEmamH41VXpf9XgnsFmnpAEgMy+hTLL21+qp9/cp\nJkmSJEkT1K/EYXNKbcMXMnNGXeGqzBcpTZY271NMkiRJkiaoX4nDitXjFePY5g8t20qSJEmaIvqV\nODxVPS4yjm0aZZ/qWkqSJEnSwPUrcbijetxuHNu8sXr8a9dSkiRJkgauX4nDryj9FQ6IiFfVFY6I\n9YEDKP0izulTTJIkSZImqF+Jw1HAE8BiwPkRcXBErNxaKCKeHxEHARcCz662ObpPMUmSJEmaoL7M\n45CZd0XEXsAplOThEOCQiPgbcB+lZmEF4PnVJlE9997MvLsfMUmSJEmauL7NHJ2Z34uIB4H/AV5Q\nPb1ytbS6C9g7M22mJEmSJE1BfUscADLz7IhYHXgL8AZgbWCZavWDwHXAucCPM/OZfsYiSZIkaeL6\nmjgAVAnBGdUiSZIkaR7Us8QhIp5T/fh0Zv5zHNstBiwMkJmP9CoeSZIkSb3Tk1GVIuIAYEa1vGmc\nm78JeAiYEREf6EU8kiRJknpr0olDRCwKfLr69euZeeZ4tq/KH0cZWWkkIhaebEySJEmSeqsXNQ5v\noXR4fpwy7OpEHAI8CixX7U+SJEnSFNKLxGH76vGnmfmPiewgM+8HfkqpdXhzD2KSJEmS1EO9SBw2\nokzedvYk99PYfqNJ7keSJElSj/UicVixerx9kvv5a/X4/K6lJEmSJA1cLxKHZ1ePMye5n0db9idJ\nkiRpiuhF4jCjelxukvtZtmV/kiRJkqaIXiQOf68eN5jkftavHu+Z5H4kSZIk9VgvEoeLKaMhvXWS\n+9mV0sn6kklHJEmSJKmnepE4/Lx63Cgi3jaRHVTbvaplf5IkSZKmiEknDpl5NnANpdbhxIjYYjzb\nR8SWwDcptQ1XV/uTJEmSNIX0osYBYF/gKWBx4NcRcXRErN5tg4hYIyKOAc6ttnsK+HCP4pEkSZLU\nQwv1YieZeWlE7E2pOViAkkh8KCJuAq4E7gUeowy1ugKwIbAmpZYigFnA3pl5WS/ikSRJktRbPUkc\nADLzlIi4E/gusBIlIVirWtqJ6vEe4O2ZeUGvYpEkSZLUW71qqgRAdfG/BqXJ0ZXAbEZrFZqX2dX6\nfYE1TBokSZKkqa1nNQ4NmfkE8DXgaxGxJLAOZXK3JSmzSz8A/CkzJzvTtCRJkqQB6Xni0KxKDi7t\n52tIkiRJ6r+eNlWSJEmSND2ZOEiSJEmqZeIgSZIkqZaJgyRJkqRaJg6SJEmSapk4SJIkSapl4iBJ\nkiSplomDJEmSpFomDpIkSZJqmThIkiRJqmXiIEmSJKmWiYMkSZKkWiYOkiRJkmqZOEiSJEmqZeIg\nSZIkqZaJgyRJkqRaJg6SJEmSapk4SJIkSapl4iBJkiSplomDJEmSpFomDpIkSZJqmThIkiRJqmXi\nUCMi3hERs6tlzw5lNo2IsyLigYh4PCKujYj9IsLjK0mSpGnBC9suImIV4KvATCA7lNkZuBB4LXBm\nVX5h4Ejg+4OJVJIkSeovE4fuvgXcDxzfbmVELAl8A3gG2CIz987MTwDrAZcBu0bE2wYVrCRJktQv\nJg4dRMR+wJbAe4DHOxTbDVgO+H5mXt14MjOfAg4CAvhAfyOVJEmS+s/EoY2IeBlwOHBUZl7cpehW\nlCZM57RZdxEl4dg0IhbufZSSJEnS4Jg4tIiIBYFTgNuBT9cUX6t6vKl1RWbOAm4DFgJW72GIkiRJ\n0sAtNOwApqBDgFcCm2XmkzVll6oeH+6wvvH80r0ITJIkSRoWaxyaRMSrgU8BX87M3w87HkmSJGmq\nMHGoVE2UTgZuBA5uXd1hs0aNwlId1jeef2gccXRcRkZGxrobSZIkzadGRkY6Xk9ORmS2nZ5gvhMR\nSwEzKJ2d2x3V5uePysyPRsQpwL8B/5aZp7bsb0FKYrEwsERmPl3z+gnQr89j9ETpx/6rfY/0YddN\n+51Xz9X+Hnvw+EuSpLFqXJdk5rizCPs4jHoSOKHDug2A9YHfUmokLquePw94O7AdcGrLNlsAiwMX\n1CUNkiRJ0lRn4lDJzCeAfdqti4hDKInDSZn5zaZVZwBHAP8aEcdm5pVV+UWAwyi3mI/ra+CSJEnS\nAJg4jN1c1TmZOTMi9gZOBy6IiB8ADwI7AWsCp2fm6YMNU5IkSeo9O0ePXdsG3pn5E0qzpAuBXYB9\ngaeAA4D/N7DoJEmSpD6yxmEMMvNQ4NAu6y8DdhhcRJIkSdJgWeMgSZIkqZaJgyRJkqRaJg6SJEmS\napk4SJIkSapl4iBJkiSplomDJEmSpFomDpIkSZJqmThIkiRJqmXiIEmSJKmWiYMkSZKkWiYOkiRJ\nkmqZOEiSJEmqZeIgSZIkqZaJgyRJkqRaJg6SJEmSapk4SJIkSapl4iBJkiSplomDJEmSpFomDpIk\nSZJqmThIkiRJqmXiIEmSJKmWiYMkSZKkWiYOkiRJkmqZOEiSJEmqZeIgSZIkqZaJgyRJkqRaJg6S\nJEmSapk4SJIkSapl4iBJkiSplomDJEmSpFomDpIkSZJqmThIkiRJqmXiIEmSJKmWiYMkSZKkWiYO\nkiRJkmqZOEiSJEmqZeIgSZIkqZaJgyRJkqRaJg6SJEmSapk4SJIkSapl4iBJkiSplomDJEmSpFom\nDpIkSZJqmThIkiRJqmXiIEmSJKmWiYMkSZKkWiYOkiRJkmqZOEiSJEmqZeIgSZIkqZaJgyRJkqRa\nJg6SJEmSapk4SJIkSapl4iBJkiSplomDJEmSpFomDpIkSZJqmThIkiRJqmXiIEmSJKmWiYMkSZKk\nWiYOkiRJkmqZODSJiGUiYq+IODMibo6IxyPioYj4bUTsGRHRYbtNI+KsiHig2ubaiNgvIjy+0jQX\nEQNZJEkatoWGHcAUsxtwHPA34HzgDmAFYBfgBGA74G3NG0TEzsAZwD+BU4EHgR2BI4FNgd0HFLsk\nSZLUNyYOc7oR2DEzf9H8ZEQcCPwBeGtE/Etm/qh6fkngG8AzwBaZeXX1/GcoiceuEfG2zDxtkG9C\n0hCMzGP7lSRpnGxK0yQzL2hNGqrn7wOOBwLYsmnVbsBywPcbSUNV/ingoKr8B/oZsyRJkjQIJg5j\n93T1+EzTc1sBCZzTpvxFwOPAphGxcJ9jkyRJkvrKxGEMImJBYA9KknB206q1qsebWrfJzFnAbZTm\nYKv3O0ZJkiSpn0wcxuYI4BXALzLz3Kbnl6oeH+6wXeP5pfsVmCRJkjQIdo6uEREfAT4K/Bl415DD\nkTRODmUqSVJvWOPQRUTsCxwFXAdsnZkPtRRp1CgsRXuN51u36/aaHZeRkZHxhC9JkqT50MjISF/m\nBTJx6CAi9geOAf5ISRrua1PsxupxzTbbLwisRulMfetYXzczOy4mDtJkZJ8WSZKmlpGRkY7Xk5Nh\n4tBGRHwC+C/gKmCrzLy/Q9HzKEOubtdm3RbA4sAlmfl0m/WSJEnSPMPEoUU1edvhlAnftsnMGV2K\nnwHcD/xrRGzYtI9FgMMotyOP62O4kiRJ0kDYObpJROwBHEppXnQJsF+btmC3Z+ZJAJk5MyL2Bk4H\nLoiIHwAPAjtRmi+dnpmnDyp+SZIkqV9MHOa0KqWWYEFgvw5lLgROavySmT+JiC2ATwO7AIsCfwEO\nAL7az2AlSZKkQTFxaJKZh1JqHMa73WXADr2PSJIkSZoa7OMgSZIkqZaJgyRJkqRaJg6SJEmSapk4\nSJIkSapl4iBJkiSplomDJEmSpFomDpIkSZJqmThIkiRJqmXiIEmSJKmWiYMkSZKkWiYOkiRJkmqZ\nOEiSJEmqZeIgSZIkqZaJgyRJkqRaJg6SJEmSapk4SJIkSapl4iBJkiSplomDJEmSpFomDpIkSZJq\nmThIkiRJqmXiIEmSJKmWiYMkSZKkWiYOkiRJkmqZOEiSJEmqZeIgSZIkqZaJgyRJkqRaJg6SJEmS\napk4SJIkSapl4iBJkiSplomDJEmSpFomDpIkSZJqmThIkiRJqmXiIEmSJKmWiYMkSZKkWiYOkiRJ\nkmqZOEiSJEmqZeIgSZIkqZaJgyRJkqRaJg6SJEmSapk4SJIkSapl4iBJkiSplomDJEmSpFomDpIk\nSZJqmThIkiRJqmXiIEmSJKmWiYMkSZKkWiYOkiRJkmqZOEiSJEmqZeIgSZIkqZaJgyRJkqRaJg6S\nJEmSapk4SJIkSaq10LADkCRNXxHR99fIzL6/hiTJGgdJkiRJY2CNgyRpAPpRK9D/2gxJ0ihrHCRJ\nkiTVssZBkjRP63c/CvtQSFJhjYMkSZKkWtY4SJLmbSPz2H4laR5ljYMkSZKkWiYOPRARK0fENyPi\n7oh4IiJui4gjI2LpYccmSVK/jIyMDDuE+ZrHf3jm12MfdvqanIhYHbgMWA74MXAjsDGwNXADsFlm\nzhjDfhL61wlvtPNgH4dEHOnDrpv2O6+eq/099uDx787jP1x+90xvEeHxGSKP//DMy8e+8b2cmeMe\nWcIah8k7jpI0fDgz35qZB2bmNsCRwEuBzw81OkmSJKkHTBwmoapteANwe2b+d8vqQ4DHgHdGxGID\nD06SpD5q3LWMiL4ukqYOE4fJ2ap6/FXrisx8FLgEWBx4zSCDkiRJknrN4VgnZy1Kw92bOqy/mVIj\nsSZw/qCCkiRpYHfrR+ax/UqaMGscJmep6vHhDusbzzu6kiRJkuZp1jhMMf2/Q9TH/Y/0b9cwwLtn\nfdPn+Ef6u3uPf42R/u7e49/FSP92DdPh2PfZSH937/HvzuMzPPPjsbfGYXIaNQpLdVjfeP6hAcQi\nSZIk9Y01DpNzI+U22pod1r+keuzUB+L/TGQsXUmSJGlQnABuEqrhWP8C3JaZa7SsWwK4p/p1+cz8\n56DjkyRJknrFpkqTkJm3UoZiXTUi9m1Z/Vng2cDJJg2SJEma11njMElVrcMlwPLAT4H/pczbsCVw\nA7BZZs4YWoCSJElSD5g49EBErEypYdgOWJbSROlM4LOZ2WmoVkmSJGmeYeIgSZIkqZZ9HCRJkiTV\nMnGQJEmSVMvEQZIkSVItEwdJkjRhEfFfEbHbsOOQ1H/OHK1xi4jFKEPOrgksXT39EGWG7Mudt0LS\noEXEMsAsR7Ibiv2BJYDThx2INAgR8WpgY2Ax4Dbg7MycOdyoBsPEQWMWEc8FPg+8E1i8Q7HHI+Jk\n4CDnr9B0ExH/Qpmj5RnKP4pzO5TbA9gjM7ceYHjTWjXs9aeAlwDXAkdk5gMRsR5wMvCKqtwlwD6Z\necPQgp1GImLPMRZdq7lsZn6zTyEJiIh1gBFgc8pks7cCpwBfycxnhhjatBER21G+7z+dmbOq55YD\nTgO2aCk+IyL2yswfDzbKwXM4Vo1JRCwNXAq8FHiMMundzUDj7t5SlH/om1G+xG4ANvHu3/BExJeA\nXTJzjWHHMq+LiABOBd4KRPV0Ar8A3pWZD7WUPwQ4ODMXHGig01RVm3AtsHLT09cAb6welwX+DDyf\nMhnn34C1Wz8XjV9EzKac62PeBEjP/d6IiL8BX87M/2p6bnPgLOa+gZfALzJzpwGGOG1FxNnAcpm5\nUdNzF1CStbuAc4AZwNqU76JnKJP+XjH4aAfHGgeN1SGUpOFI4JDMfLRdoYhYgjIZ3v7AwcC/DyxC\ntVoOWHXYQUwT7wF2Be4EjgeeBvYAdgAujoitM/O+IcY33e1LSRr+k3K3byfK98y3gZmUmxR3AETE\n5yk1Ex8GPjeMYKehRynn/eNt1gXlu/4q4GeDDGo+sSKlGRgAEbEA8C1KE5mvUD6XfwCbAMcCb46I\nt2fmd4cQ63SzDvDzxi8R8RpK0nAO5abcP5vWbUu5kfRJyv+KacsaB41JRNwG3JKZ24yx/HnAapm5\nWn8jUycR8S3K3XDv/E1SRPyW0hTmpY0EISIWBI4APgpcB2ydmfdX66xx6KGIuAp4OjNf3fTcRZQa\nzl0y8ydNzwelNvSB5vKamIh4B/BV4H7gPZl5cZsys4ETMnOfQcc33VXHdiQzP1v9viVwHnB8Zn6w\npeyqlJq332bmGwcb6fQTEU9QansOqn7/COXm6bqZeX2b8mcAm2fm8oONdLCscdBYrQR8fxzlLwc2\n7VMs86Wq78h4ePx7Zx3gjOZaharN68ci4g7gKODXEbGVfXv64kXAd1qeu4KSOFza/GRmZkRcCOwy\noNimtcz8TnU8vwVcEBFHUdp8Pznk0OZX61KaJB3buiIzb4+IX1DuimvyZlBq7hsWrR5v61D+Vkot\n9LRm4qCxegBYaxzlX1Zto955B+UfRtQVbGKVYm88C7i33YrMPKa6K3gMcG5EjKlWTuOyGKVvVbOH\nATLzH23K30vpa6UeyMw7gW0iYj/gcGD7iHh3Zv5+yKHNjxrn9a0d1t9CacqnybsceFNELFR1OL+e\n8v/3lcBlbcqvD9wzwPiGwnkcNFbnAG+JiA/WFYyIfSlfXGf3Par5y0xKp/OtxricM5wwp6W7gRd2\nWpmZx1KaLG1AOe5LDSiu+cX9lE7PzR4DOvUrWZYyRLR6KDOPBjak9HW4JCIOj4iFhxzW/KD5BtAd\n1eOSHcouydxJtibmWGAV4OsRsRDlmuY64LiIWKW5YETsD2wN/HTgUQ6YfRw0JtVQiFdRqu1uB35F\nmbeheVSlNYFtKR1y7wM2ysy7Bx3rdFW16X5lZo7potQ+Dr0TEWcCG2fmC2rKfYJyR/YZYEGPfW9E\nxK+BxTNzTM3vIuJXlNFQNuhvZPOnqn/PIZRO6DdSaphPtI9D71W1mQ8xmggvQukw/frMvKBN+Z8D\nq2fmywcW5DQWEV8EPgb8Ffgh8BTwccoAGVdTPpeXU24s3QlsmJnTurWFTZU0Jpl5d0RsAhwHvAF4\nH3M3g2k0ofkV8EGThp67BtgsItbIzFuGHcx85ixKjdubM/MXnQpl5hER8SzgUGwm1ktXAvtHxLMy\n86luBSPiOcBrgRMGEtl8qOrfc3DVnv5kxtd8UuNzB3M2UX2qeu51wAXNBSNicUr/Bke36pHM/I+I\nuBk4jFKr3PgsFqSMZEX13M+AD033pAGscdAERMTqlKYwazHaJONhyp2n8zOzU9tLTUJEvBU4CNg/\nMy8cQ/mdgfUy89C+BzfNVfMI7Abc2O4uX5vyewCreuwHLyJeAmwP/LrdyCfqrar2YQngycx8Ytjx\nzM8i4qXA7pT/wxcNO57ppLoh9AbgVZRmkwtQahtuBH7TGA56fmDiIEmSJKmWnaMlSZIk1TJxkCRJ\nklTLxEGSJElSLRMHSZIkSbVMHCRJkiTVMnGQJEmSVMvEQZIkSVItEwdJkiRJtUwcJE1LEXFBRMyO\niPOGHctUFhGrRMRxEXFzRPyzOmazI+Jdw45tXhMRWzQdv82HHY8k9ZqJgzTNtFy8zI6IH49hm0Oa\nyq85iDgHIKtFHUTEKsBVwPuA1YFnMYHj1nL+NC9PRsR9VVLyy4g4LCJe3/t3MuVM6fOuKaluXZ6J\niAcj4qqIOCYi1h52rHUiYrGI+EsV/8MRsfIYt9u96X1/s99xStOFiYM0fTUuXnaMiI3Guc10EcMO\nYIr7DLAs8AzwSWBTYJ1qqU0428iWZaFq/6sD2wIHAudWF3p7Tjr6AWm6wDx42LH0SOvn1FgCWAp4\nJbAvcE1EjAwpxjHJzH8C76XEvwTw9bptImIZ4Jhqm7uBA/oZozSdLDTsACQNxGHAdsMOQlPO6ykX\nTz/OzC/1aJ97An+ofg7gOZTkYUPKObgxJZE4ISJ2AHbPzKd79Nr9NB2T6gTWZjTBXgBYCdiJUgu1\nIPCZiPhbZv7PUKIcg8y8MCL+hxLzmyLi7Zn53S6bHAM8j/L+P5iZDw8iTmk6sMZBmt7+QbkoeENE\nvHbYwWjKaTTruLGH+7wtM/9cLddn5mWZ+fPMPDQzNwG2AG6nXLTtDJzQw9fWOGXm/zZ9Xtdl5rmZ\n+WFgd0YTikMjYqrX3n0cuJMS81ER8bx2hSJie+DfKOffDzLzZ4MLUZr3mThI09uxwOPVz58bZiCa\nkp5VPQ7sjn9mXgy8Gvgb5SLvHRHx5kG9vsYmM38EXEL5jJYHNhhuRN1l5qPAPtWvy1C+++YQEUsA\nx1W/3g98ZDDRSdOHiYM0vd1LqZYPYPOI2GYiOxnrCEURsUdVblZEvLDN+tubOyNGxAYR8d2IuCMi\nHq860X4lIpZt2W7TiDg9Iv5ajfzzl4j4QnUhMNb38JKIOD4ibqle6+8R8eOI2GqM2y8RER+PiAsj\n4t6q4+/fq06/74qIjt+nbd73+hFxYlMssyPiOWN9L037XSgi9omIc6tYnqxi+3VEvC8i5mqO2vQZ\nzWa0XftISyfZvo5ElZn/AN7f9NSB3cpHxIsi4ksRcXVEzKjOgb9GxPeiZvSiiFg6It4dEadExPUR\nMbM6TvdExNkRsXdELNxh29trjlNtx9qIeGv1+dzbdO4eHREr1Gy3QkR8PiL+UL3np6p9XBcRP6w+\n9+W67aMHLm/6+UUd4nxeRHw2In4XEfdHxBMRcVdEnBkRO3bacUQs2HQMD6ye2zoiTqs+2ycj4r7x\nBJuZ5wAnUT6rXSPiLS1FvgisQvk8983MB7rtLyJ2afnemRERV0TEoVH6SXTbdv0ogwacGxF3V+/n\nkYi4ISK+ERHr1Wx/ZHVsHqx+X6Z63cbfgCOfaTgy08XFZRotlKYgs4FZlDtwzwUeqn6/rMM2hzRt\ns2ab9edX686ree09mvbzwjbrb6vWfRN4B/BE9XvzMhu4AVi+2uZjbco0yv0BWLxDLP8XM6Vt/cwO\n+5gNfLbmfW1OScJmd4nlEmC5Dts3v++9gSfb7OM54/ycVwH+1CGmxvu6DlilzWfUWq51+9+MM5bm\n82fzcWx3Y9N2K3Qos191nnR7n8cB0WH722s+t9nAlY3zrcPnNqvLPk7s8Le3FXByl7jvBtboEPNm\nwINjiHufCX5HnN/Yd025w5ti2K3N+v8HPFLz2fwQWLTNtgs2bXcg8J9t9nPfBN7b0tWxbRzjpZr+\nhhv7/WHNPpYDLqo5/vd3OtcpTfA6/W01n0uf6BLDkVW5Byn9UO5qs793TeTzd3GZzGLnaGmay8wZ\nEXEk5eJu44jYITN/PoFd9bKN83qUdsY3AV+mXOAuSelY+07gJcCXI+JHlLuEl1KaHtxI+af+EeDN\nlOYTB9H9jvXKwPco/2g/Q7loeoZycfZJSjOMT0fEXdmmA2hEvAb4FbAw5WLhq8DVlH/kzwPeQkkG\nNgF+FBFbZuasDrFsXL2/u6r3/QfKcd0EeKrLe2iNaXHgN8CLKXdPzwK+QWnj/QJgL2AH4OXAeRGx\nXmY+Vm3+I0Y7L19XbX8c8N9NL/EYg3Eu5bMGeB1wRvPKiPgo5TglcD0lzpson8PqlPf5RkqCZiUo\nLQAADeRJREFU/AjwiTavEcBlwC8on9u9lCZaq1GS1+0o5+MPgK1btn1DVbbTcQKY0eG9fY7yuf4M\n+DYlCVkWeDfl3F+Rkkhu0fKeFwZOpYxuNBM4npL83kcZ0ORFlKZerXfT+2Hdpp//1hLn7sB3ql//\nSvm7uJ5yfF8AvB14GyXOE6vfO3lb9VrXAkdRjveiwKvGG3BmPhQRH6Sc5ysCR0bEByh9aYJyIf7B\nTttXf1sXAS+lfE98Bzib8vktBLyWMgrTisDPImKjzLy5ZTcLAQ8DPwUupHxvPVpt80rK99dKwH9G\nxA2Z+ZMub2lh4ExK86svA7+k3Ah6CeW4S4M17MzFxcWltwstNQ7Vc0tSLrZmAVe12WYsNQ6z6V2N\nw2zKP+d2dyJPq9Y/XcV8Ki13kynNLC+tyt0HLNAl5tmUi7uXtSnzQsoF0WzKP+PntqxfCLi1ivnX\nwLM7vO/tKRcZs4D31LzvP1LdBZ3EZ3xE03H+UocyX2gq8+UOZRrrD55kPBOtcdizabsDW9a9lNGa\nmcO77KPxPp8GXtxmfdu7+h3O2a0mc5xa/vZmAZ/pUO7EpnLrtKzbqmnd9jWvN6HziDHUOAAbVcd0\nNiUpe1bTuucxWov5bWChDvvYt+m9vK5lXXONw2zgHGDhyZyHLfv/ftP+f9X08ztrtvsqo98r63Qo\ns2LT98JP2qxfvtN3RbV+UUoN5Wzgmg5lGjUOsyk1bpv06ti4uExmsY+DNB/IzJnAlyh33F4ZEbsO\nMZyg/DPcKzOfaLO+cUd3AWAR4H2ZOcdQmJk5G2jUDixLubPeSQKfy8z/nWtF5h2M3qVeEmhtM7w7\nsCrlAuodOXrXvnU/Z1GaZATlYridxvCXkxr+sbojvVe1r1sotSbtfJpypzOA90bEIhN9zT5qbmPe\n2mb8Y5S7rX/KzE912cdBlORvAUoSMIfMvKVbAJl5EnBN9Wsv7+JfnZmdBiT4YtPPW7SsW7Hp54u6\nvcBkzqN2olipukN/DuXiPoGjM7O5RuxDlGF276XcnHimQ3zHUmp5oPvfxTPAntnbYXk/TLnxALAN\n5X38MjNP6bRBlL5VjTkhPpmZf2pXLjP/TqnlDODNrX1NMvO+Tt8V1fongMY5vU5ErNblfSRwbGZe\n1qWMNDAmDtL84xjKP3oY7vCKCfwxM2/qsP7app/PzcyHxlBu9ZrX+3aX9acx2jTnDS3rdq4eL60u\nFrppXOS9Kjp3lL4zy6hCk7ERpd8KwEnZoVlU9fy3ql+fQ2neMtU82vTzki3rdqR8dmd220F10XoZ\no02+uqo6Hb8kIl7RWCht4YPSjKRXOs4jkJmNpisw97nb3CToPT2Mp63mjt6UO+h3A1+j9BVIykSA\nIy2b7VSt+3lLQtHORXT/bBL4bWbePbF30GGnmfdTkodGwj6TMs9DN2+k1AZAuRHQTePvOIDXdCsY\nEYtGxAsj4mVN51zzzZC6867bnBTSQNnHQZpPZOY/I+JwShvil1Lad3e8+9ZnnZIGKE0gxluu9aKz\n2W2Z+WCnlZn5ZET8kXJhs27L6o0o/+C3rC6sxmJhyt3z+1ueT0ozpclau+nnyzuWmnv9OtTcwR6C\n5s/tkcYPUUbkakzQNRJjn714xXZPRhnu9f2UDrLdzpVejlI0Vw1XixnAs5k7nkuAv1D6rxwdEe+k\nXLxfBPwhM5/sYYzQfmK7J4DfAV/PzFObV1Q1Xo2/k70iYq8xvk7bz6ZybZd1k3EGpckSwO/HkJxs\n1PTzjHHcW5nrvUUZJe2jwK6U79tuN2q7nXe9+t6QesLEQZq/HE9pAvIC4OCI+F6nO9Z99ninFZmZ\nTf+wO5ajNHdqWLBLubEM6dioiVm25fnlG2GNYR8NCSzeYV2njrTj0dykp+69NdeSdB0+ckiaL5ia\nk7vlm34ez7FfrPWJiDiB0WYy2WV/0W77Seh27sLo+TvHuZuZz0SZUft0SpK4IaMXtE9GxKWUzv4n\n96hpT/PM0bMod+b/XjUHbGdZykVwt2PZTrdj24u/i16Y6Hk3x997RLyM0idqpab9tNtf47h3OzaP\nDek7WmrLxEGaj2TmUxFxGCWBWJ1yQfWN4UbVd+O5AGjVuKj7DbD/OLbrdGez1xcAk3lvU0HzpGLN\ns1c3X0x/gbE31Zij2UxEvJdyjielrf3RlDvpdwOPN/rORMRJlNGupsTsyFUzvldGxJsozeU2B9ai\njPC0VbV8PCK2z8xbJ/ladTUjrZo/m28DXxnrS3VZN1UujBvvLZm79rGbexo/VE1Af0BJGmZRRuI6\nkzLE9AONZC8instoH59u591UOTYSYOIgzY++CfwHJXE4KCK+PYZtGncf6/pFPXsScfVL14m2Wsq0\nTgh1P/B8yuhPf+5pVBPXfGd+BcrQlZ00N6Ho2FxriJonJPxt08/NzbxmTeLYN5rR/AXYrEszn6lY\nG0Nm/pIy/CZVB9w3UNrpv44yHOepTGDI0klq/huJKfR30QuN8y4otS4T+ZvZmNIsMIH/yMwjO5Sb\nkuecVMfO0dJ8pupM+tnq1xcAHxjDZjOrx+d2LVXa8k41q3Wb5TUinkW5u5iUCdWaXU25iNggIhZt\n3XZImhOFug7PzevbjhAzLNWswo15KC7JMpt0w22UcfChjJs/UY1OqD+t6RuwQZd1U0Jm3p+Z38/M\nLSnDizbOy24DA/Qjjicod8+DMhfKdHJ1088TPe9e0fTzaV3KbdRlnTRlmThI86fvMPrP/5N0bpPf\n0GgOsWZELNGuQHUB/taeRdg7QZthOpvszmhNybkt6xoTMy1G/Ygsg3IFo23C39lpBKeIWJDRUXke\noTTRmRIiYnnmnEjt8Ob1Vfv6n1M+u80jYr0JvlSjVr1jTVhEvIU526K30xg2eKoMaXte08+97NA9\nVo2/ixdXHc+ni19Shl6GMmP5RDS35OhWAztVvk+kcTFxkOZD1YXZSPXrCpTZbLu5sHp8Fp3b+n+N\ncgE2FX2m6rA4h4hYhdGL1keBk1qKnEyZnTUos7xu2+1FImLdqmNr31RtpL9RxbQmZYbidg6j1AAl\ncEIfRuOZkIjYnJLErEyJ7ZSqSU6rwynj+y8AnFYz1j0RsUNErN3y9M2U47RjRCzdZps1KDOSJ93b\nmTfasK/RLYZeiIjXRsSLu6wP4PXVrwnc3u+Y2jiS8vcSwAkR0XU40YjYPCImU3M0EJl5D2VyvqCM\npPbFbuUjYpmIeH/L082zSL+7w3afAraceKTS8NjHQZpPZeZpEXEgpZlO3V3LX1Caj6xGmQNiOcpQ\nh49TOm1+ENiUMrb5VLpASMo/8uWBy6oLgfMpHQ43o0z+tnxV7hOZOcfoLpn5dETsRkmcFgXOiogf\nUsZ4v7XabnlKU5edKO3Nv0y5W95PnwP+hdLO/VPVBfMJwF2U5md7A40E5hbmHoe/n1aLiOZOn0tS\nzq8NgDdR2oBDOXY/osQ6l8z8c0QcQJl/5MXAtRFxIqWZzj2Uu/8voIyhvyvwIsp7bm7KdTJl4sOV\ngcsj4ohq/aKUi+/9KMnwVZTRizq5lHLu7xQR+1CGTG3UQjzS0sxqsl5PSXQvBs6iDFV6H+X9rk7p\nt7El1RwXmTmWUcN6KjPvi4g9KCM/rQD8LiJOpnxP3EnpZPx8yt/DLpQE9v2Mzn0wlX2M0aGZPxYR\n21D+tq6hzPeyNKU50tbAmynv9/im7X9LSeZWBT4REStR+qLcSzmH9qTMND/VviulMTFxkOZvB1PG\niO86mkw1ROTbKbPJLgF8pFr+rwjlDvHN1P8zHOTINUGZUGt/Snvjw1rWN4aU/EJmHk8bmXlFRLyO\ncpG0KrBbtcxVtFo6zebbs/edmY9FxNaUC8u1KZOl7dgmnuuB7bvNYttjweikc+00jtFtwGGZ+e1u\nO8vMr0XETEqtwLMpF/rtmpAkpXai9X0eTemAvS0lyTqxZf1jlNnCd6B74vBlSjO8RZjzIhHKyEKd\nZkWu0+mcCEoH6M3brGscwwvokHQNQmb+qOqnchJliNa9GO2MPkdRRidgG5Yx/+1l5uMRsSUl6dyB\nMjnbse2KVo9z/L1X35XvoDR7WoLSTHKPlu0up5x3kxoRSxoGEwdpehrTGOuZ+dOI+D2jI7N03CYz\nL4+IDYADKRdjK1BG6vk98NXM/E11F7Lutcc7/ns3Y3qtzDw7IjYC/p0S+0qUC5nLgKMz8/yuL5J5\nVUSsRZk0b2fK3fPnVasfoAwlejHw48y8ZoKxjktm3l19HntSEpl1KXdDH6ZMGHU6cOIAx4Bv996e\nphznhykjG10BnJeZ57Up236nmSdHxM8pbcK3BV5G6aT/FGWeiuspbf5/2DrBV3UR92bKAADvAl5O\nuYi8m9Kf5ejMvLlqXtbx88nMayNiE+DjlJqqFRjt79C6zXg+53Zlv0i5u70NsD7lzv0KVdz3AlcC\n38vMrjNqT/C1x7eDzF9WTcj2otxFX5syWtAs4B/Anym1dT/MzFu6xNFP3eZRaL9B5sPAztUNg3dR\nPvPnU/o6PUJJfP9ASQ7mamaXmZdGxPrApygjYa1I+Ru4iTIh3dcpSUVdXD39zpB6IaphrCVJkiSp\nIztHS5IkSapl4iBJkiSplomDJEmSpFomDpIkSZJqmThIkiRJqmXiIEmSJKmWiYMkSZKkWiYOkiRJ\nkmqZOEiSJEmqZeIgSZIkqZaJgyRJkqRaJg6SJEmSapk4SJIkSapl4iBJkiSplomDJEmSpFomDpIk\nSZJqmThIkiRJqmXiIEmSJKmWiYMkSZKkWv8f2cgp1KpGB8cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117eacf28>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 271,
       "width": 391
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "horse_kicks[[\"Predicted Instances (Poisson)\",\"Observed Instances\"]].plot.bar()\n",
    "plt.xlabel(\"Number of Deaths Per Year\",size=14)\n",
    "plt.ylabel(\"Count\",size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The message here is that when events occur at random, we actually tend to perceive them as clustered.   \n",
    "\n",
    "Here is another example:\n",
    "\n",
    "![](figs/pinker-glow-worms-and-stars-plot.jpg)\n",
    "\n",
    "Which of these was generated by a random process ocurring equally likely everywhere?\n",
    "\n",
    "These images are from Steven Pinker’s book, _The Better Angels of our Nature._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In the left figure, the number of dots falling into regions of a given size follows the Poisson distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Uniform Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The uniform distribution models the case in which all outcomes are equally probable.  \n",
    "\n",
    "It can be a discrete or continuous distribution.\n",
    "\n",
    "We have already seen the uniform distribution in the case of rolls of a fair die:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"665a382bcb200c17\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#665a382bcb200c17\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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BRwA/Bw6IiMe1VqEkSZI0AMMMDJtN8fHZ0BlB2LKyvPP4zZO001n+3cz8WfeC5mTpLzbf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\n6w+A70TEO1n/CfwTmza2adp4ZWa2Nev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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aaf4d68>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 270,
       "width": 390
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "plt.figure()\n",
    "x = np.arange(7)\n",
    "plt.plot(x, 7*[1/6.], 'bo', ms=8)\n",
    "plt.vlines(x, 0, 1/6., colors='b', lw=5, alpha=0.5)\n",
    "plt.xlim([-0.5,6.5])\n",
    "plt.ylim([0,1.1])\n",
    "plt.xlabel('Number of points showing',size=14)\n",
    "plt.ylabel(r'$P[X = x]$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "There is an important relationship between the uniform and Poisson distributions.\n",
    "\n",
    "__When the time an event occurs is uniformly distributed, the number of events in a time interval is Poisson distributed.__\n",
    "\n",
    "You can replace \"time\" with \"location\", and so on.\n",
    "\n",
    "Also, the reverse statment is true as well.\n",
    "\n",
    "So a simple way to generate a picture like the scattered points above is to select the $x$ and $y$ coordinates of each point uniformly distributed over the picture size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Gaussian Distribution\n",
    "\n",
    "The Gaussian Distribution is also called the Normal Distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We will make __extensive__ use of Gaussian distribution, for a number of reasons.\n",
    "\n",
    "One of reasons we will use it so much is that it is a good guess for how errors are distributed in data.\n",
    "\n",
    "This comes from the celebrated __Central Limit Theorem__.   Informally, \n",
    "\n",
    ">_The sum of a large number of independent observations from any\n",
    ">distribution with finite variance tends to have a Gaussian\n",
    "> distribution._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "As a special case, the sum of $n$ independent Gaussian variates is Gaussian.\n",
    "Thus Gaussian processes remain Gaussian after passing through linear\n",
    "systems.   \n",
    "\n",
    "If $X_1$ and $X_2$ are Gaussian, then $X_3 = aX_2 + bX_3$ is Gaussian."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Thus we can see that one way of thinking of the Gaussian is that it is the\n",
    "limit of the Binomial when $n$ is large, that is, the limit of\n",
    "the sum of many Bernoulli trials.    However many other\n",
    "sums of random variables (not just Bernoulli trials) converge to the\n",
    "Gaussian as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The _standard Gaussian_ distribution has mean zero and a variance (and standard deviation)\n",
    "of 1.   The pdf of the standard Gaussian is:\n",
    "\n",
    "$$ p(x) = \\frac{1}{\\sqrt{2 \\pi}} e^{-x^2/2}. $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For an arbitrary Gaussian distribution with mean $\\mu$ and variance\n",
    "$\\sigma^2$, the pdf is simply the standard Gaussian that is relocated to\n",
    "have its center at $\\mu$ and its width scaled by $\\sigma$:\n",
    "\n",
    "$$ p_{\\mu,\\sigma}(x) = \\frac{1}{\\sigma \\sqrt{2 \\pi}} e^{-\\frac{1}{2}\\left(\\frac{x-\\mu}{\\sigma}\\right)^2}. $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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IiEjRPPggvPIKbLklDB+edDTJ6thxbTJ28cUhORMRqUVKQEREpCjc4bLLwvyF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ab13320>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 287,
       "width": 400
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import norm\n",
    "plt.figure()\n",
    "x = np.linspace(norm.ppf(0.001), norm.ppf(0.999), 100)\n",
    "plt.plot(x, norm.pdf(x),'b-')\n",
    "plt.title(r'Standard Gaussian PDF.  $\\mu = 0, \\sigma = 1$',size=14)\n",
    "plt.xlabel('x',size=14)\n",
    "plt.ylabel(r'$p(x)$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"5641c0c453af975b\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#5641c0c453af975b\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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UVLfeCltsUcZKbL01XH55Wd1a0thjMiFJkprm5pvLInRPPQXbbw+XXAJzzFF1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\nsA8/nPeTuPXWoiuSJNUi50y0XL/S/YMLPpFS+gR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      "text/plain": [
       "<matplotlib.figure.Figure at 0x117e7d518>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 287,
       "width": 393
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "plt.figure()\n",
    "x = np.linspace(norm.ppf(0.001), norm.ppf(0.999), 100)\n",
    "plt.plot(x, norm.cdf(x),'b-')\n",
    "plt.title(r'Standard Gaussian CDF.  $\\mu = 0, \\sigma = 1$',size=14)\n",
    "plt.xlabel('x',size=14)\n",
    "plt.ylabel(r'$P[X\\leq x]$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Heavy Tails"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Earlier we discussed high- and low-variability.   \n",
    "\n",
    "All of the distributions we have discussed so far have \"light tails\", meaning that they show low variability.\n",
    "\n",
    "In other words, extremely large observations are essentially impossible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "However in other cases, extremely large observations can occur.   Distributions that capture this property are called \"heavy tailed\".\n",
    "\n",
    "Some examples of data that can be often modeled using heavy-tailed distributions:\n",
    "\n",
    "* The sizes of files in a file system\n",
    "* The sizes of objects transferred over the Internet\n",
    "* The execution time of jobs on a computer system\n",
    "* The degree of nodes in a network (eg, social network).\n",
    "\n",
    "In practice, random variables that follow heavy tailed distributions\n",
    "are characterized as exhibiting many small observations mixed in with\n",
    "a few large observations.  \n",
    "\n",
    "In such datasets, most of the observations\n",
    "are small, but most of the contribution to the sample mean or variance\n",
    "comes from the rare, large observations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### The Pareto Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The Pareto distribution is the simplest continuous heavy-tailed\n",
    "distribution.    \n",
    "\n",
    "Pareto was an Italian economist who studied income distributions.\n",
    "(In fact, income distributions typically show heavy tails.)\n",
    "\n",
    "Its pdf is:\n",
    "\n",
    "$$ p(x) = \\alpha k^{\\alpha} x^{-\\alpha-1}\\;\\;\\; k \\leq x,\\; \\;0 < \\alpha\n",
    "\\leq 2. $$\n",
    "\n",
    "It takes on values in the range $[k, \\infty]$. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
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       "            if (p.length==0) return;\n",
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     "metadata": {},
     "output_type": "display_data"
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    {
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     "output_type": "stream",
     "text": [
      "\n"
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    {
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Prx+fHxHn1M/vyMy31c8XA9dQLQ27S68fMYh2SpIkSU010oEC2At4XdvPCexcH1CFh7d1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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b520eb8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 286,
       "width": 394
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import pareto\n",
    "alpha = 1.3\n",
    "x = np.linspace(pareto.ppf(0.005,alpha), pareto.ppf(0.995,alpha), 100)\n",
    "plt.plot(x, pareto.pdf(x,alpha),'b-', lw=5, alpha=0.6, label='pareto pdf')\n",
    "plt.title(r'Pareto PDF.  $\\alpha$ = {}'.format(alpha),size=14)\n",
    "plt.xlabel(r'x',size=14)\n",
    "plt.ylabel(r'p(x)',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The variance of the Pareto distribution is infinite.  (The corresponding\n",
    "integral diverges.)\n",
    "\n",
    "In practice, this means that a new observation that significantly\n",
    "changes the sample variance is _always_ possible, no matter how many samples\n",
    "of the random variable have already been taken."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The mean of the Pareto is $\\frac{k\\alpha}{\\alpha-1}$, for $\\alpha > 1$.  \n",
    "\n",
    "But\n",
    "note that as $\\alpha$ decreases, the variability of the Pareto\n",
    "increases.  \n",
    "\n",
    "In fact, for $\\alpha \\leq 1$, the Pareto distribution has\n",
    "_infinite mean._  Again, in practice this means that a swamping\n",
    "observation for the mean is always possible.   \n",
    "\n",
    "Hence the running average\n",
    "of a series of Pareto observations with $\\alpha \\leq 1$ will never\n",
    "converge to a fixed value, and the mean itself is not a useful\n",
    "statistic in this case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Statistics: \"The collection, analysis, interpretation, and presentation of masses of data.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Bayes' Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Bayes' Rule is a simple way of manipulating conditional probabilities in a way that can be very useful."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Start with a situation in which we are interested in two events, $A_1$ and $A_2$.  These are exhaustive, meaning that in any experiment either $A_1$ or $A_2$ must occur. (They form a partition of $\\Omega$.)\n",
    "\n",
    "Now:\n",
    "\n",
    "$$ P[A_1|B] = \\frac{P[A_1 \\cap B]}{P[B]}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$ = \\frac{P[A_1 \\cap B]}{P[B|A_1] + P[B|A_2]}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$ = \\frac{P[B|A_1]\\,P[A_1]}{P[B|A_1] + P[B|A_2]}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "(This is easy to extend to the case where $A_1, A_2, ..., A_n$ form a partition of $\\Omega$.)\n",
    "\n",
    "This formula is useful because often the probabilities $P[B|A_i]$ can be\n",
    "estimated, while the probabilties $P[A_i|B]$ may be hard to estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We interpret this transformation as updating our estimate of the probability of each $A_i$\n",
    "based on new information, namely, that $B$ is true.   \n",
    "\n",
    "This update\n",
    "transforms the __prior__ probabilities $P[A_i]$ into the \n",
    "__posterior__ probabilities $P[A_i|B]$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Example.__\n",
    "\n",
    "Empirical evidence suggests that amongs sets of twins,\n",
    "about 1/3 are identical.  \n",
    "\n",
    "Assume therefore that probability of a pair of\n",
    "twins being identical to be 1/3.  \n",
    "\n",
    "Now, consider how a couple might\n",
    "update this probability after they get an ultrasound that shows that the\n",
    "twins are of the same gender.   \n",
    "\n",
    "What is their new estimate of the\n",
    "probability that their twins are identical?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let $I$ be the event that the twins are identical.  Let $G$ be the event\n",
    "that gender is the same via ultrasound.  \n",
    "\n",
    "The prior probabilities here\n",
    "is $P[I]$.\n",
    "\n",
    "What we want to calculate is the\n",
    "posterior probability $P[I\\,|\\,G]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "First, we note:\n",
    "\n",
    "$$P[G\\,|\\,I] = 1 $$\n",
    "\n",
    "(Surprisingly, people are sometimes confused about that fact!)   \n",
    "\n",
    "Note that this conditional probability is easy to estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Also,\n",
    "we assume that if the twins are not identical, they are like any two\n",
    "siblings, _i.e.,_ their probability of being same gender is 1/2: \n",
    "\n",
    "$$P[G\\,|\\,\\bar{I}] = 1/2 $$\n",
    "\n",
    "Again, easy to estimate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "And we know from observing the population at large that among all sets\n",
    "of twins, about 1/3 are identical:\n",
    "\n",
    "$$ P[I] = 1/3 $$\n",
    "\n",
    "Note that this statistic is easy to obtain from data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Then:\n",
    "\n",
    "$$ P[I\\,|\\,G] = \\frac{P[G\\,|\\,I]\\; P[I]}{P[G\\,|\\,I]\\,P[I] + P[G\\,|\\,\\bar{I}]\\,P[\\bar{I}]} $$\n",
    "\n",
    "$$ = \\frac{1 \\cdot 1/3}{(1 \\cdot 1/3) + (1/2 \\cdot 2/3)} = \\frac{1}{2}$$\n",
    "\n",
    "So we have updated our estimate of the twins being identical from 1/3\n",
    "(prior probability) to 1/2 (posterior probability).\n",
    "\n",
    "We did this in a way that used quantities that were relatively easy to obtain or measure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Confidence Intervals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Say you are concerned with some data that we take as coming from a random process.\n",
    "\n",
    "You want to characterize it as accurately as possible.   You measure it, yielding a\n",
    "single value.  \n",
    "\n",
    "How much does that value tell you?   Can you rely on it as a description of the random process?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's say you have a dataset and you compute its average value.   \n",
    "\n",
    "How certain are you that the average would be the same if you took another dataset from the same source (i.e., the same random process)?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We think of the hypothetical data source as a random variable with a true mean $\\mu$.\n",
    "\n",
    "We would like to find a range within which we are 90% sure that the\n",
    "true mean $\\mu$ lies.  \n",
    "\n",
    "In other words, we want the probability that the true mean lies in\n",
    "the interval to be 0.9.  This interval is then called the 90% confidence interval."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To be more precise:  A confidence interval at level $\\gamma$ for a fixed\n",
    "but unknown parameter $m$ is an interval $(a,b)$ such that\n",
    "\n",
    "$$ P[a < m < b] \\geq \\gamma. $$\n",
    "\n",
    "Note that $m$ is fixed --- it is not random.  What is random is the\n",
    "interval $(a, b)$.  This interval is constructed based on the\n",
    "data, which (by assumption) are random."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "![](figs/confidence-intervals.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Confidence Intervals for the Mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Imagine we have a set of $n$ samples of a random variable,\n",
    "$x_1, x_2, ..., x_n$ Let's assume that the random variable has mean\n",
    "$\\mu$ and variance $\\sigma^2$.\n",
    "\n",
    "An estimate of $\\mu$ is the empirical average of the samples, $\\bar{x}$.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now, the Central Limit Theorem tells us that the sum of a\n",
    "large number $n$ of random variables, each with mean $\\mu$ and variance\n",
    "$\\sigma^2$, yields a Gaussian random variable with mean\n",
    "$n\\mu$ and variance $n \\sigma^2$.   So the distribution of the average\n",
    "would be normal with mean $\\mu$ and variance $\\sigma^2 / n$.  That\n",
    "is, \n",
    "\n",
    "$$ \\bar{x} \\sim N(\\mu, \\sigma/\\sqrt{n}) $$\n",
    "\n",
    "We usually assume that the number of samples should be 30 or more for\n",
    "the CLT to hold.   While the specific value 30 is a bit shaky, we will usually be\n",
    "using very large samples (datasets) in this course for which this assumption is \n",
    "valid."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The standard deviation of the sample mean is called the standard error.\n",
    "\n",
    "Notice that the standard error decreases as we increase the sample size, according to $1/\\sqrt{n}.$\n",
    "\n",
    "So it will turn out that using $\\bar{x}$, we can get\n",
    "increasingly \"tight\" estimates of $\\mu$ as we increase the number of\n",
    "samples $n$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now, remember that the true mean $\\mu$ is a constant, while the\n",
    "empirical mean $\\bar{x}$ is a random variable.   \n",
    "\n",
    "Let us assume for a\n",
    "moment that we know the true $\\mu$ and $\\sigma$, and that we accept that\n",
    "$\\bar{x}$ has a $N(\\mu, \\sigma/\\sqrt{n})$ distribution.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Then it is\n",
    "true that \n",
    "\n",
    "$$ P[\\mu-k\\sigma/\\sqrt{n} < \\bar{x} < \\mu+k\\sigma/\\sqrt{n}] = P[-k < S <\n",
    "k]$$\n",
    "\n",
    "where $S$ is the standard Gaussian random variable (having distribution $N(0,1)$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We write $z_{1-\\alpha/2}$ to be the $1-\\alpha/2$ quantile of the\n",
    "unit normal.  That is, \n",
    "\n",
    "$$ P[-z_{1-\\alpha/2} < S < z_{1-\\alpha/2}] = 1-\\alpha.$$\n",
    "\n",
    "So to form a 90% probability interval for $S$ (centered on\n",
    "zero) we choose $k = z_{0.95}$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
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    "slideshow": {
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NghIREZG1VNxI6FHXcf8m9H09DphG6GmnP3CMmfVz9yU5VpFpndsC1xHqFq/T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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117ec5cc0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 286,
       "width": 400
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "from scipy.stats import norm\n",
    "plt.figure()\n",
    "x = np.linspace(norm.ppf(0.001), norm.ppf(0.999), 100)\n",
    "x90 = np.linspace(norm.ppf(0.05), norm.ppf(0.95), 100)\n",
    "plt.plot(x, norm.pdf(x),'b-')\n",
    "plt.fill_between(x90, 0, norm.pdf(x90))\n",
    "plt.title(r'90% region for Standard Gaussian',size=14)\n",
    "plt.xlabel('x',size=14)\n",
    "plt.ylabel(r'$p(x)$',size=14)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Turning back to $\\bar{x}$, the\n",
    "90% probability interval on $\\bar{x}$ would be:\n",
    "\n",
    "$$ \\mu-z_{0.95}\\sigma/\\sqrt{n} < \\bar{x} <\n",
    "\\mu+z_{0.95}\\sigma/\\sqrt{n}. $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The last step: by a simple argument, we can show that the sample mean is \n",
    "in some fixed-size interval centered on the true mean, if and only if the true\n",
    "mean is also in\n",
    "a fixed-size interval (of the same size) centered on the sample mean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This means that:\n",
    "\\begin{eqnarray*}\n",
    "  1-\\alpha & = & P[\\mu-z_{1-\\alpha/2}\\sigma/\\sqrt{N} < \\bar{x} <\n",
    "\\mu+z_{1-\\alpha/2}\\sigma/\\sqrt{N}]\\\\\n",
    "& = & P[\\bar{x}-k\\sigma\\sqrt{N} < \\mu < \\bar{x}+k\\sigma/\\sqrt{N}].\n",
    "\\end{eqnarray*}\n",
    "This latter expression defines the __$1-\\alpha$ confidence interval\n",
    "  for the mean.__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We are done, except for estimating $\\sigma$.  We do this\n",
    "directly from the data: $\\hat{\\sigma} = s$\n",
    "(where $s$ is the sample standard deviation, $s = \\sqrt{1/(n-1) \\sum (x_i\n",
    "- \\bar{x})^2}$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To summarize: by the argument presented here, a 100(1-$\\alpha$)%\n",
    "confidence interval for the population mean is given by\n",
    "\n",
    "$$\\bar{x} \\pm  z_{1-\\alpha/2} \\, \\frac{s}{\\sqrt{n}}. $$\n",
    "\n",
    "As an example, a 95% confidence interval for the mean is the sample average plus or minus two standard errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Confidence Intervals for the Median"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A $p$th percentile of a distribution is the value $m_p$ such that $P[X <\n",
    "m_p] = p$.   For example, the median is the 50th percentile."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Say we start with a set of $n$ i.i.d. observations of an RV $X$. \n",
    "\n",
    "The true $p$th percentile of $X$ is $m_p$ by definition.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Each observation\n",
    "$X_i$ therefore has probability $p$ of being below the corresponding\n",
    "percentile $m_p$.  \n",
    "\n",
    "What is the probability that exactly $j$ of the\n",
    "observations are less than $m_p$?  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This is a standard coin-flipping\n",
    "problem --- it is given by the Binomial: $B_{n,p}(j)$.\n",
    "\n",
    "$$ P[\\mbox{exactly }j\\mbox{ observations are less than } m_p] = B_{n,p}(j). $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "  \n",
    "We can write this compactly using _order statistics._  For a set\n",
    "of values $X_1, X_2, ..., X_n$ the order statistics are obtained by\n",
    "simply sorting the set.  This yields $X_{(1)}, X_{(2)}, ..., X_{(n)}$ ---\n",
    "so that, for example, $X_{(1)}$ is the smallest of the values and\n",
    "$X_{(n)}$ is the largest."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Then the above expression can be written:\n",
    "\n",
    "$$ P[X_{(j)} < m_p \\leq X_{(j+1)}] = B_{n,p}(j). $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now we can string consecutive intervals together if we like, yielding:\n",
    "\n",
    "$$ P[X_{(j)} < m_p \\leq X_{(k)}] = \\sum_{i=j}^k B_{n,p}(i). $$"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Now look at this from another standpoint.  \n",
    "\n",
    "The above expression also\n",
    "can be read as giving the probability that the $p$th percentile lies between\n",
    "$X_{(j)}$ and $X_{(k)}$.   "
   ]
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   "source": [
    "Let's say the sum on the right evaluates to\n",
    "$\\gamma$.   \n",
    "\n",
    "Then we have shown that $(X_{(j)}, X_{(k)})$ is a confidence\n",
    "interval at level $\\gamma$ for $m_p$."
   ]
  },
  {
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   "source": [
    "To use this in practice, let's say we have a set of $n$ measurements and\n",
    "we want to find the $\\gamma$ confidence interval for $p$th percentile.\n",
    "\n",
    "Then we just \n",
    "need to find integers $j$ and $k$ so that \n",
    "\n",
    "$$ \\sum_{i=j}^k B_{n,p}(i) \\geq \\gamma. $$"
   ]
  },
  {
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   "source": [
    "This can be aided if we have a table of the cumulative distribution of\n",
    "the binomial $F_{n,p}(k)$.   Then we need to find $j$ and $k$ such that\n",
    "\n",
    "$$ F_{n,p}(k) -  F_{n,p}(j) \\geq \\gamma. $$\n",
    "\n",
    "(Remember also that when $np$ is large, we can approximate the binomial\n",
    "by the Normal distribution)."
   ]
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   "source": [
    "__Example.__  Let's say we want the 95% confidence interval for the\n",
    "median, based on the following dataset:\n",
    "\n",
    "3, 1, 9, 7, 11, 15, 12, 4, 17, 10.\n",
    "\n",
    "We can compute that for $n = 10$ and $p = 0.5$,  $F_{n,p}(9) -\n",
    "F_{n,p}(2) \\geq 0.95$.  The order statistics are:\n",
    "\n",
    "1, 3, 4, 7, 9, 10, 11, 12, 15, 17.\n",
    "\n",
    "Then our estimate of the median is 9.5, and the confidence interval is (3,\n",
    "15)."
   ]
  }
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