Repaso estadística.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Estadística\n",
    "\n",
    "\n",
    "\n",
    "<img src=\"images/meme.jpeg\" alt=\"drawing\" width=\"500\"/>\n",
    "\n",
    "¿Por qué queremos estudiar estadística?\n",
    "\n",
    "En Machine Learning trabajamos con observaciones de ciertos sucesos o fenónemos, los cuales utilizamos como atributos para realizar predicciones. Estas observaciones podemos verlas como variables aleatorias (v.a) que provienen de cierta distribución. Por ejemplo, si queremos predecir la nota final de los alumnos en el ramo de Machine Learning, podemos tener como un atributo su estatura. Supongamos que observamos todas las estaturas de los alumnos y obtenemos lo siguiente:\n",
    "\n",
    "$Obs = \\{1.51, 1.66, 1.85, 1.63, 1.72, 1.75\\}$\n",
    "\n",
    "A partir de esta información, podemos asumir que nuestras observaciones provienen de una distribución normal. Denotaremos nuestras observaciones como las variables aleatorias $x_{1}, x_{2}, ... x_{n} \\in X$, las cuales son i.i.d.\n",
    "\n",
    "$X \\sim \\mathcal{N}(\\mu, \\sigma^{2})$\n",
    "\n",
    "De esta manera podemos transformar problemas de predicción en problemas estadísticos, modelando el problema anterior en la forma: $P(Y|X)$, donde $Y$ es la v.a. que representa la nota final del alumno.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([162.8935425 , 178.73360704, 171.47853579, 165.57064747,\n",
       "       183.16196618, 186.46431469, 160.0635735 , 198.04810373,\n",
       "       168.08738239, 177.64946444, 185.99318891, 171.62797083,\n",
       "       183.98799126, 183.34376099, 169.92133435, 169.98177172,\n",
       "       180.26937028, 185.51735126, 150.13302459, 159.11845716])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "\n",
    "mu, sigma = 170, 10\n",
    "x = np.random.normal(mu, sigma, 20)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probabilidades\n",
    "\n",
    "Las probabilidades son el lenguaje matemático para cuantificar la incerteza. \n",
    "\n",
    "$\\textbf{Notación: }$\n",
    "1. Espacio muestral ($\\Omega$): Espacio de los posibles resultados de un experimento. \n",
    "2. Realización ($\\omega$): Posible resultado de un experimento, dado el espacio muestral $\\Omega$.\n",
    "3. Eventos: Subconjunto de posibles resultados de la realización de un experimento, dado el espacio muestral $\\Omega$.\n",
    "\n",
    "Ejemplo: Si tiramos dos monedas al aire, $\\Omega = \\{CC, CS, SC, SS\\}$. Un evento en el que la primera moneda sale cara es: $A=\\{CS, CC\\}$.\n",
    "\n",
    "$\\textbf{Operadores: }$\n",
    "1. Evento complementario: $A^{c} = \\{\\omega \\in \\Omega: \\omega \\notin A \\}$\n",
    "2. Union: $\\cup^{n}_{i=1}A_{i} = \\{\\omega \\in \\Omega: \\omega \\in A_{i}$ para al menos un $i\\}$\n",
    "3. Intersección: $\\cap^{n}_{i=1}A_{i} = \\{\\omega \\in \\Omega: \\omega \\in A_{i}$ para todos los $i\\}$\n",
    "4. Diferecia: $A-B = \\{\\omega: \\omega \\in A, \\omega \\notin B\\}$\n",
    "5. Eventos disjuntos: $A_{i}\\cap A{j} = \\emptyset$\n",
    "\n",
    "$\\textbf{Definición: }$\n",
    "\n",
    "La probabilidad es la asignación de un valor real al nivel de certeza que tenemos sobre la realización de un evento. Podemos calcularla:\n",
    "\n",
    "$P(A) = \\frac{Realizaciones\\ de\\ A}{Realizaciones\\ totales}$\n",
    "\n",
    "$\\textbf{Axiomas}$:\n",
    "\n",
    "1. $P(A) \\geq 0$ para cada A.\n",
    "2. $P(\\Omega) = 1$\n",
    "3. Si $A_{1}, A_{2}, ... , A_{n}$ son disjuntos: $P(\\cup^{n}_{i}A_{i}) = \\sum ^{n}_{i=1}P(A_{i})$\n",
    "\n",
    "$\\textbf{Otras propiedades:}$\n",
    "\n",
    "Estas pueden ser derivadas a partir de los axiomas anteriores.\n",
    "\n",
    "1. $P(\\emptyset) = 0$\n",
    "2. $A \\subset B \\Rightarrow P(A) \\leq P(B)$\n",
    "3. $P(A^{c}) = 1 - P(A)$\n",
    "4. $P(A) \\cup P(B) = P(A) + P(B) - P(A \\cap B)$\n",
    "5. Dos eventos son independientes si $P(A,B) = P(A)P(B)$\n",
    "\n",
    "\n",
    "**Nota**: Desde ahora denotaremos como $P(A,B)$ a la intersección $P(A\\cap B)$\n",
    "\n",
    "\n",
    "$\\textbf{Teorema:}$\n",
    "Si $A_{n} \\rightarrow A$, entonces $P(A_{n}) \\rightarrow P(A)$ mientras $n \\rightarrow \\infty$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-2.5, 2.5, -2.5, 2.5]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Circle, Polygon\n",
    "%matplotlib inline\n",
    "\n",
    "plt.figure(figsize=(8,8))\n",
    "\n",
    "plt.gca().add_artist(plt.Rectangle((-2,-2),4,4, edgecolor='r', hatch='///', fill=None))\n",
    "\n",
    "plt.gca().add_artist(plt.Circle((0,0),1,color='c'))\n",
    "\n",
    "\n",
    "plt.text(-0.2, 0., \"$P(A)$\", color=\"k\", fontsize=20)\n",
    "plt.text(-1.5, 1.5, \"$P(A^{c})$\", color=\"k\", fontsize=25)\n",
    "\n",
    "\n",
    "plt.axis([-2.5, 2.5, -2.5, 2.5])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sabemos que el área de una circunferencia puede ser calculada como:\n",
    "\n",
    "$A_{cir} = \\pi r^{2}$\n",
    "\n",
    "A su vez el área de un cuadrado:\n",
    "\n",
    "$A_{sq} = h^{2}$\n",
    "\n",
    "Por lo tanto, la $P(A)$ está dado por:\n",
    "\n",
    "$P(A) = \\dfrac{\\pi}{4^{2}} \\sim 0.1963 $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(A) = 0.2\n",
      "P(A) = 0.19518209408194234\n",
      "P(A) = 0.2007593735168486\n",
      "P(A) = 0.19756915870101918\n",
      "P(A) = 0.19786324786324785\n",
      "P(A) = 0.1945067051627854\n",
      "P(A) = 0.19350957733101157\n",
      "P(A) = 0.1963742943986105\n",
      "P(A) = 0.19861793830590582\n",
      "P(A) = 0.19679986490194837\n",
      "P(A) = 0.19638650353370318\n",
      "P(A) = 0.1958444160420049\n",
      "P(A) = 0.1968303225091433\n",
      "P(A) = 0.1962469309014381\n",
      "P(A) = 0.19435170860136253\n",
      "P(A) = 0.1974185866825419\n",
      "P(A) = 0.19562532655678525\n",
      "P(A) = 0.19564342714084537\n",
      "P(A) = 0.1965652279468423\n",
      "P(A) = 0.19542\n"
     ]
    }
   ],
   "source": [
    "ns = np.linspace(10, 100000, num=20, dtype='uint')\n",
    "\n",
    "\n",
    "for n in ns:\n",
    "    x = np.random.uniform(-2,2, n)\n",
    "    y = np.random.uniform(-2,2, n)\n",
    "    ixs = np.where(np.sqrt(x**2 + y**2) <= 1)[0]\n",
    "    count_a = len(ixs)\n",
    "\n",
    "    print('P(A) = {}'.format(count_a/n))\n",
    "    \n",
    "\n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10fbc80b8>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))\n",
    "\n",
    "plt.scatter(x, y, c='r', s=3)\n",
    "plt.scatter(x[ixs], y[ixs], c='c', s=3, alpha = 0.7)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probabilidades condicionales\n",
    "\n",
    "La probabilidad condicional de A dado B es:\n",
    "\n",
    "$P(A|B) = \\dfrac{P(A,B)}{P(B)}$\n",
    "\n",
    "$\\textbf{Obs}$: En general: $P(A|B) \\neq P(B|A)$\n",
    "\n",
    "Ej: La falacia del prosecutor.\n",
    "\n",
    "Supongase que un test medico para una enfermedad $D$ tiene resultados positivos ($+$) y negativos ($-$). Las probabilidades para cada caso son:\n",
    "\n",
    "\n",
    "|- | $D$| $D^{c}$ |\n",
    "| --| ------------- | ------------- |\n",
    "|+| 0.0081  | 0.0900  |\n",
    "|-| 0.0009  | 0.9010  |\n",
    "\n",
    "La probabilidad de que una persona salga positivo dado que tiene la enfermedad es:\n",
    "$P(+|D) = \\dfrac{P(+,D)}{P(D)} = \\dfrac{0.0081}{0.0081+0.0009} = 0.9$\n",
    "\n",
    "\n",
    "La probabilidad de que una persona salga negativo dado que no tiene la enfermedad es: $P(-|D^{c}) = \\dfrac{P(-,D^{c})}{P(D^{c})} = \\dfrac{0.9010}{0.9010+0.09} = 0.9$\n",
    "\n",
    "\n",
    "Al parecer el test es bastante preciso! Supongamos que nos hacemos el test y salimos positivo. ¿Cual es la probabilidad de que tengamos la enfermedad?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Teorema de Bayes\n",
    "\n",
    "Sabemos que: $P(A,B) = P(B,A)$, por lo tanto:\n",
    "\n",
    "$P(A|B)P(B) = P(B|A)P(A)$\n",
    "\n",
    "Entonces:\n",
    "\n",
    "$P(A|B) = \\dfrac{P(B|A)P(A)}{P(B)}$\n",
    "\n",
    "- $P(A|B)$: Posteriori.\n",
    "- $P(B|A)$: Verosimilitud.\n",
    "- $P(A)$: Priori.\n",
    "- $P(B)$: Marginal. Es llamada así porque se puede obtener marginalizando sobre A en la forma: $P(B) = \\sum^{n}_{i=1}P(B|A_{i})P(A_{i})$ (Ley de la probabilidad total).\n",
    "\n",
    "\n",
    "\n",
    "Monty Hall problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variables aleatorias\n",
    "\n",
    "Matemáticamente una variable aleatoria es un mapeo: $X: \\Omega \\rightarrow \\mathbb{R}$, que asigna un valor real $X(\\omega)$ a cada realización $\\omega$.\n",
    "\n",
    "Ejemplo: Sea $X(\\omega)$ la cantidad de caras en una secuencia $\\omega = CCSSCSCSSC$, entonces $X(\\omega) = 5$.\n",
    "\n",
    "Podemos asignar una probabilidad a las variables aleatorias de la siguiente forma:\n",
    "\n",
    "\n",
    "|$\\omega$ | $P(\\omega)$| $X(\\omega)$ |\n",
    "|--| ------------- | ------------- |\n",
    "|CC| $\\frac{1}{4}$  | $0$  |\n",
    "|CS| $\\frac{1}{4}$  | $1$  | \n",
    "|SC| $\\frac{1}{4}$  | $1$  |\n",
    "|SS| $\\frac{1}{4}$  | $2$  |\n",
    "\n",
    "\n",
    "\n",
    "|$x$ | $P(X=x)$|\n",
    "|--| ------------- | \n",
    "|0| $\\frac{1}{4}$  |\n",
    "|1| $\\frac{1}{2}$  |\n",
    "|2| $\\frac{1}{4}$  |\n",
    "\n",
    "\n",
    "\n",
    "$\\textbf{Definición}$: La **función de distribución cumulativa (CDF)**, $F_{X}: \\mathbb{R} \\rightarrow [0,1]$ de una variable aleatoria X está definida por: \n",
    "\n",
    "$$F_{X}(x)=P(X \\leq x)$$\n",
    "\n",
    "$\\textbf{Teorema}$: Una función $F_{X}: \\mathbb{R} \\rightarrow [0,1]$ es un CDF para una medida de probabilidad $P$ si y sólo si:\n",
    "1. $F$ es no-decreciente: $x_{1} \\leq x_{2}$ implica que: $F(x_{1}) \\leq F(x_{2})$\n",
    "2. $F$ es normalizada: $\\lim_{x \\rightarrow -\\infty}F(x)=0$ y $\\lim_{x \\rightarrow \\infty}F(x)=1$\n",
    "3. $F$ es derecho-continua: $F(x)=F(x^{+})$ para todo $x$ donde: $F(x^{+}) = \\lim_{y \\rightarrow x} F(y)$\n",
    "\n",
    "\n",
    "¿Cuál es la función cumulativa para el caso de las monedas?\n",
    "\n",
    "$$ f_{X}(x)=   \\left\\{\n",
    "\\begin{array}{ll}\n",
    "      0 & x<0 \\\\\n",
    "      \\frac{1}{4} & 0\\leq x < 1\\\\\n",
    "      \\frac{3}{4} & 1\\leq x < 2\\\\\n",
    "      1 & x > 2\\\\\n",
    "\\end{array} \n",
    "\\right.  $$\n",
    "\n",
    "$\\textbf{Definición}$: Para una variable **discreta**, la **función de masa de probabilidad (PMF)** de una variable aleatoria X está definida por: \n",
    "\n",
    "$$f_{X}(x)=P(X = x)$$\n",
    "\n",
    "Para una función discreta, es posible caracterízar su PMF a partir de la probabilidad de cada variable aleatoria. En el caso de las monedas:\n",
    "$$ f_{X}(x)=   \\left\\{\n",
    "\\begin{array}{ll}\n",
    "      \\frac{1}{4} & x=0 \\\\\n",
    "      \\frac{1}{2} & x=1\\\\\n",
    "      \\frac{1}{4} & x=2 \\\\\n",
    "      0 & x \\notin \\{0,1,2\\}\\\\\n",
    "\\end{array} \n",
    "\\right.  $$\n",
    "\n",
    "\n",
    "$\\textbf{Propiedades}$:\n",
    "1. $f_{X}(x) \\geq 0$ para todo $x \\in \\mathbb{R}$.\n",
    "2. $\\sum_{i} f_{X}(x_{i})=1$\n",
    "\n",
    "\n",
    "$\\textbf{Definición}$: Para una variable **continua**, existe una función $f_{X}$ tal que: $f_{X}(x) \\geq 0$ y para todo $x$, $\\int_{-\\infty}^{\\infty}f_{X}(x)dx=1$. Para todo $a<b$:\n",
    "\n",
    "\n",
    "$$P(a<X<b) = \\int_{a}^{b}f_{X}(x)dx$$\n",
    "\n",
    "\n",
    "la **función de densidad de probabilidad (PDF)** de una variable aleatoria continua X definida por: \n",
    "\n",
    "$$F_{X} = \\int_{-\\infty}^{x}f_{X}(t)dt$$\n",
    "\n",
    "donde $f_{X}(x) = F'_{X}(x)$ para todos los $x$ donde $F_{X}$ es diferenciable.\n",
    "\n",
    "\n",
    "¿Cómo definimos el CDF para variables discretas y continuas?\n",
    "\n",
    "$P(X\\leq k)=\\sum^{k}_{i=1}P(X=i)$\n",
    "\n",
    "$P(X\\leq k)=\\int_{-\\infty}^{k}f_{X}dx$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esperanza\n",
    "\n",
    "La esperanza o media de una variable aleatoria $X$, denotada por $\\mathbb{E}$ o $\\mu$, es el valor promedio para $X$. Esto es definido matemáticamente como:\n",
    "\n",
    "$$ \\mathbb{E}(X) = \\left\\{\n",
    "\\begin{array}{ll}\n",
    "      \\sum_{x} x f(x) & si\\ X\\ es\\ discreto \\\\\n",
    "      \\int_{x} x dF(x) & si\\ X\\ es\\ continuo \\\\\n",
    "\\end{array} \n",
    "\\right. $$\n",
    "\n",
    "**Propiedades**:\n",
    "1. $\\mathbb{E}(Y) = \\mathbb{E}(r(X)) = \\int_{x}r(x)f_{X}(x)dx$ $\\leftarrow$ LOTUS: Law of the unconscious statistician.\n",
    "2. $\\mathbb{E}\\big(\\sum_{i}X_{i}\\big)=\\sum_{i}\\mathbb{E}(X_{i})$, si $X_{1},...,X_{n}$ son independientes.\n",
    "3. $\\mathbb{E}\\big(\\prod_{i}X_{i}\\big)=\\prod_{i}\\mathbb{E}(X_{i})$, si $X_{1},...,X_{n}$ son independientes.\n",
    "4. $\\mathbb{E}\\big(aX\\big)=a\\mathbb{E}(X)$, si $a$ es una constante.\n",
    "\n",
    "\n",
    "## Varianza \n",
    "\n",
    "La varianza, denotada por $var(x)$ o $\\sigma^{2}$, mide la dispersión de una distribución, es decir, que tan alejada estará una v.a $X$ desde su media o esperanza.\n",
    "\n",
    "$$var(X) = \\mathbb{E}\\big(X-\\mathbb{E}(X)\\big)^{2} = \\int_{x}\\big(x-\\mathbb{E}(X)\\big)^{2}dF(x) = $$\n",
    "\n",
    "**Propiedades**:\n",
    "1. $var(X) = \\mathbb{E}\\big(x-\\mathbb{E}(X)\\big)^{2} = \\mathbb{E}\\big(X^{2}-2X\\mathbb{E}(X) + \\mathbb{E}(X)^{2}\\big) = \\mathbb{E}X^{2}-2\\mathbb{E}(X)\\mathbb{E}(X) + \\mathbb{E}(X)^{2} = \\mathbb{E}(X^{2}) - \\mathbb{E}(X)^{2}$\n",
    "2. $var(aX) = a^{2}\\cdot var(X)$, si $X_{1},...,X_{n}$, si $a$ es una constante.\n",
    "3. $var(X+a) = var(X)$, si $a$ es una constante.\n",
    "4. $var\\big(\\sum_{i}X_{i}\\big) = \\sum_{i}var(X_{i})$, si $a$ es una constante.\n",
    "\n",
    "\n",
    "Podemos definir la **media muestral** ($\\bar{X_{n}}$) y **varianza muestral** $S^{2}_{n}$ como sigue:\n",
    "\n",
    "$\\bar{X}_{n} = \\dfrac{1}{n}\\sum^{n}_{i=1}X_{i}$\n",
    "\n",
    "$S_{n}^{2} = \\dfrac{1}{n-1}\\sum_{i=1}^{n}(X_{i} - \\bar{X})^{2}$\n",
    "\n",
    "Esto es verdad por la ley de los grandes números:\n",
    "\n",
    "$\\bar{X}_{n} = \\dfrac{1}{n}\\sum^{n}_{i=1}X_{i} \\rightarrow \\mu$ as $n \\rightarrow \\infty$\n",
    "\n",
    "Demostración:\n",
    "\n",
    "Primero definimos la convergencia en probabilidad: Una secuencia de variables aleatoria $X_{1}, X_{2}, ...$ denotada como $X_{n}$ converge en probabilidad a la variable aleatoria $X$ si:\n",
    "$$P(|X_{n}-X|>\\epsilon)\\rightarrow 0, \\forall \\epsilon > 0, si\\ n\\rightarrow \\infty$$\n",
    "\n",
    "Entonces: \n",
    "\n",
    "$$P(|\\bar{X}_{n}-\\mu|>\\epsilon) \\leq \\dfrac{V(\\bar{X_{n}})}{\\epsilon^{2}},\\ (desigualdad\\ de\\ Chebyshev)$$ \n",
    "$$P(|\\bar{X}_{n}-\\mu|>\\epsilon) \\leq \\dfrac{\\sigma^{2}}{n\\epsilon^{2}}$$\n",
    "Finalmente:\n",
    "$$P(|\\bar{X}_{n}-\\mu|>\\epsilon) \\leq 0,\\ si\\ n \\rightarrow \\infty$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribuciones conocidas:\n",
    "\n",
    "### Distribución Uniforme Discreta:\n",
    "\n",
    "$$ f_{X}(x)=   \\left\\{\n",
    "\\begin{array}{ll}\n",
    "      \\frac{1}{k} & x \\in \\{1,...,k\\} \\\\\n",
    "      0 & x \\notin \\{1,...,k\\} \\\\\n",
    "\\end{array} \n",
    "\\right.  $$\n",
    "\n",
    "Suponiendo $x \\in [a,b]$:\n",
    "\n",
    "$\\mathbb{E}(X) = \\dfrac{a}{b-a} + \\dfrac{a+1}{b-a} + ... + \\dfrac{b}{b-a} = \\dfrac{(b-a)(b+a)}{2} \\cdot \\dfrac{1}{b-a} = \\dfrac{b+a}{2} $\n",
    "\n",
    "\n",
    "Para calcular la varianza:\n",
    "$\\mathbb{E}(X^{2}) = \\dfrac{1}{b-a+1}\\sum_{i=a}^{b}X_{i}^{2} = \\dfrac{1}{b-a+1} \\cdot \\dfrac{(b)(b+1)(2b+1)+(a-1)((a-1)+1)(2(a-1)+1)}{6}$ $\\leftarrow$ (Suma de secuencia de cuadrados)\n",
    "\n",
    "$var(X) = \\dfrac{1}{b-a+1} \\cdot \\dfrac{(b)(b+1)(2b+1)+(a-1)((a-1)+1)(2(a-1)+1)}{6} -  \\Big(\\dfrac{b+a}{2}\\Big)^{2} =\\dfrac{(b-a+1)^{2}-1}{12}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Distribución uniforme')"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0\n",
    "b = 20\n",
    "\n",
    "samples = np.random.randint(low=a, high=b, size=1000000)\n",
    "samples += 1\n",
    "unique, counts = np.unique(samples, return_counts=True)\n",
    "\n",
    "plt.bar(unique, counts)\n",
    "plt.xticks(unique, unique)\n",
    "plt.ylabel('Ocurrencias')\n",
    "plt.title('Distribución uniforme')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media estimada: 10.504596, Teórica: 10.0\n",
      "Varianza estimada: 33.26840087678402, Teórica: 36.666666666666664\n"
     ]
    }
   ],
   "source": [
    "print('Media estimada: {}, Teórica: {}'.format(np.mean(samples), (a+b)/2))\n",
    "print('Varianza estimada: {}, Teórica: {}'.format(np.std(samples)**2, ((b-a+1)**2-1)/12))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Distribución Bernoulli\n",
    "\n",
    "Una variable aleatoria $X$ se distribuye Bernoulli si tiene sólo dos posibles valores de ocurrencia (0 y 1) y se cumple que: $P(X=1) = p$ y $P(X=0) = 1-p$. El PMF está dado por:\n",
    "$$f_{X}(x)=p^{x}(1-p)^{1-x}, x \\in \\{0,1\\}$$\n",
    "\n",
    "\n",
    "$\\mathbb{E}(x) = 0\\cdot(1-p) + 1\\cdot(p) = p$ \n",
    "\n",
    "\n",
    "Para calcular la varianza:\n",
    "\n",
    "$\\mathbb{E}(X^{2}) = 0^{2}\\cdot(1-p) + 1^{2}\\cdot(p) = p$ \n",
    "\n",
    "$var(x) = p-p^{2} = p\\cdot(1-p)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Distribución Bernoulli')"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, p = 1, 0.5\n",
    "samples = np.random.binomial(n, p, size=10000)\n",
    "\n",
    "unique, counts = np.unique(samples, return_counts=True)\n",
    "\n",
    "plt.bar(unique, counts)\n",
    "plt.xticks(unique, unique)\n",
    "plt.ylabel('Ocurrencias')\n",
    "plt.title('Distribución Bernoulli')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media estimada: 0.4992, Teórica: 0.5\n",
      "Varianza estimada: 0.24999935999999998, Teórica: 0.25\n"
     ]
    }
   ],
   "source": [
    "print('Media estimada: {}, Teórica: {}'.format(np.mean(samples), p))\n",
    "print('Varianza estimada: {}, Teórica: {}'.format(np.std(samples)**2, p*(1-p)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Distribución Binomial\n",
    "\n",
    "Es la distribución de numero de sucesos de la variable aleatoria $X$ en $n$ intentps independientes, distribuidos Bernoulli con parámetro $p$. Su PMF está dado por:\n",
    "\n",
    "$$f_{X}(x)=\\dbinom{n}{x}p^{x}(1-p)^{1-x}, x \\in \\{0,...,n\\}$$\n",
    "\n",
    "\n",
    "Usando la propiedad numero 2 de la esperanza podemos encontrar la esperanza de esta distribución:\n",
    "\n",
    "$\\mathbb{E}(X)=\\mathbb{E}(\\sum_{i}X_{i})=\\sum_{i}\\mathbb{E}(X_{i}) = n \\cdot p$\n",
    "\n",
    "Usando esta misma propiedad podemos encontrar la varianza:\n",
    "\n",
    "$var(X)= var(\\sum_{i}X_{i}) = \\sum_{i}var(X_{i}) = n \\cdot p \\cdot (1-p)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Distribución Binomial')"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1QRzeaCvMzKzXaWmIKd/ueyhwSJ5e3mpZMzPbNLW0kZd0LnAma35idCvg6qYaZWZm7dfqUcCHgaNJvyZHRDwF7NhUo8zMrP1aTRAr8s30AlbfytvMzDZjrSaI6yX9G+l3oj8J/BL49+aaZWZm7dbqvZi+JelQ4CVgH+CciLi90ZaZmVlbdZogJPUFfhkRHwScFMzMthCdDjFFxCrgdUk7d2cFkvpKekDSzfn5XpJ+J6lD0k+KHx6StE1+3pHjw7uzPjMz2zhaPQexDJgpaaKkS4pHi2U/B8wqPb8QuDgi9gZeBMbm+WOBF/P8i/NyZmbWJq1+k/qG/OgSSUOAI4FvAGco3Sf8EOB/5UUmAecBlwGj8zTAZOBSScpXT5lZC4aPv6V2/pwLjuzhltjmoNVzEIdFxN93o/7vAP/Imu9M7AYsjoiV+fl8YHCeHkz6pToiYqWkJXn5tX7aVNI4YBzAsGHDutEkMzNrRacJIiJWSdpT0tYRsaLViiUdBTwbEdMkHbwhjay0ZwIwAWDkyJE+utgEeS/XbNPQ6hDT48BvJE0hf5saICK+vZ4y7wOOlnQEsC2wE/Bd0ncp+uWjiCHAgrz8AtL9nuZL6gfsDDzflRdjZmYbT6snqWcDN+fldyw91ikizoqIIRExHDgOuDMPU90FfDQvNob0a3UAU/JzcvxOn38wM2ufVr8o97WNuM4zgeskfR14AJiY508ErpLUAbxASipmZtYmLSUISXeR78NUFhGHtFI+Iu4G7s7TjwPvrVnmVeBjrdRnZmbNa/UcxJdK09sCHwFWrmNZMzPbDLQ6xDStMus3ku5toD1mZtZLtDrEtGvpaR/g3aSrjMzMbDPV6hDTNNI5CJGGlp5gzS0yzMxsM9TqENNeTTfEzMx6l1Z/k/o0Sf1Lz3eR9JnmmmVmZu3W6hflPhkRi4snEfEi8MlmmmRmZr1Bqwmib74TK7D6Bn5bN9MkMzPrDVo9Sf1fwE/y71IDfAr4RTNNMjOz3qDVBPFV0pBScd7hv1hziwwzM9sMrTdB5Luq/l/gFPJvNQDDSHd37QOsarR1ZmbWNp2dg7gI2BV4c0TsFxH7AXuRviT3raYbZ2Zm7dNZgjiKdAXT0mJGnv40cESTDTMzs/bqLEFE3W8yRMQqau7uamZmm4/OEsRDkk6qzpR0AvBwM00yM7PeoLOrmE4DbpD0CdL9mABGAtsBH26yYWZm1l7rTRARsQDYX9IhwJ/l2bdGxB2dVSxpW+BXwDZ5PZMj4lxJewHXAbuRks6JEbFC0jbAlaQ7xT4PfDwi5nTvZZmZ2YZq9WZ9dwJ3drHu14BDImKZpK2AX0v6T+AM4OKIuE7SD0h3hb0s/30xIvaWdBxwIfDxLq7Teonh42/5k3lzLjiyDS0xs+5q9VYbXRbJsvx0q/wI4BBgcp4/CTgmT4/Oz8nxUeXbe5iZWc9q9ZvU3ZLv2TQN2Bv4PjAbWBwRxc+VzgcG5+nB5C/jRcRKSUtIw1DPVeocB4wDGDZsWJPNN9vs+MjOuqKxIwhIl8NGxL7AEOC9wNs2Qp0TImJkRIwcMGDABrfRzMzqNZogCvlW4XcBfwX0z7fwgJQ4FuTpBcBQWH2Lj51JJ6vNzKwNGksQkgYUPzIkaTvgUGAWKVF8NC82BrgxT0/Jz8nxO+u+pGdmZj2jyXMQg4BJ+TxEH+D6iLhZ0kPAdZK+DjzAmrvCTgSuktQBvAAc12DbzMysE40liIiYAbyrZv7jpPMR1fmvAh9rqj1mZtY1PXIOwszMNj1OEGZmVssJwszMajlBmJlZLScIMzOr5QRhZma1nCDMzKyWE4SZmdVygjAzs1pOEGZmVssJwszMajlBmJlZLScIMzOr5QRhZma1nCDMzKyWE4SZmdVq8idHh0q6S9JDkv4g6XN5/q6Sbpf0WP67S54vSZdI6pA0Q9J+TbXNzMw61+RPjq4EvhgR90vaEZgm6XbgZOCOiLhA0nhgPHAmcDgwIj/2By7Lf82sBwwff0vt/DkXHNnDLbHeorEjiIh4OiLuz9NLgVnAYGA0MCkvNgk4Jk+PBq6M5B6gv6RBTbXPzMzWr0fOQUgaTvp96t8BAyPi6RxaCAzM04OBeaVi8/O8al3jJE2VNHXRokWNtdnMbEvX5BATAJLeAPwU+HxEvCRpdSwiQlJ0pb6ImABMABg5cmSXytrG4+EIs81fo0cQkrYiJYdrIuKGPPuZYugo/302z18ADC0VH5LnmZlZGzR5FZOAicCsiPh2KTQFGJOnxwA3luaflK9mOgBYUhqKMjOzHtbkENP7gBOBmZKm53lnAxcA10saC8wFjs2xW4EjgA5gOXBKg20zM7NONJYgIuLXgNYRHlWzfACnNdUeMzPrGn+T2szMajlBmJlZrcYvc7VNly9lNduy+QjCzMxqOUGYmVktJwgzM6vlBGFmZrV8ktrMOuULFrZMPoIwM7NaThBmZlbLCcLMzGo5QZiZWS0nCDMzq+UEYWZmtZwgzMyslhOEmZnVavInR38k6VlJD5bm7SrpdkmP5b+75PmSdImkDkkzJO3XVLvMzKw1TX6T+grgUuDK0rzxwB0RcYGk8fn5mcDhwIj82B+4LP81s17O37LefDX5k6O/kjS8Mns0cHCengTcTUoQo4Er88+O3iOpv6RBEfF0U+2zxP/cZrYuPX0OYmBpo78QGJinBwPzSsvNz/P+hKRxkqZKmrpo0aLmWmpmtoVr20nqfLQQ3Sg3ISJGRsTIAQMGNNAyMzODnk8Qz0gaBJD/PpvnLwCGlpYbkueZmVmb9HSCmAKMydNjgBtL80/KVzMdACzx+Qczs/Zq7CS1pGtJJ6R3lzQfOBe4ALhe0lhgLnBsXvxW4AigA1gOnNJUu8zMrDVNXsV0/DpCo2qWDeC0ptpiZmZd51+U2wLUXcrqy1jNrDNOEGbWKH/XZtPlezGZmVktJwgzM6vlBGFmZrWcIMzMrJYThJmZ1XKCMDOzWr7MdTPgywhtU+XPbu/mIwgzM6vlBGFmZrWcIMzMrJbPQWwiPFZrZj3NCcLMeiXvFLWfh5jMzKyWjyB6Ee8xmbXOt7FvXq86gpD0IUmPSOqQNL7d7TEz25L1miMISX2B7wOHAvOB+yRNiYiH2tuyjcdHCGY9w/9rG0evSRDAe4GOiHgcQNJ1wGigLQlifYev6/vw+YNp1rttyP/vlvb/rfRz0O0n6aPAhyLi1Pz8RGD/iDi9stw4YFx+ug/wyEZY/e7Ac92IbUjZdtTr19I76/Vr2fTWuaFlu2tj1btnRAzodKmI6BUP4KPAD0vPTwQu7aF1T+1ObEPKtqNev5beWa9fy6a3zg0t291HU/Wu69GbTlIvAIaWng/J88zMrA16U4K4DxghaS9JWwPHAVPa3CYzsy1WrzlJHRErJZ0O/BfQF/hRRPyhh1Y/oZuxDSnbjnr9WnpnvX4tm946N7RsdzVVb61ec5LazMx6l940xGRmZr2IE4SZmdXryUumesMD2Ba4F/g98Afga3n+6cBsIIAHK7FrgEeB5cALldjEXNfMHJtZjpfWuRBYVSl7BTAHeBl4Ja+/iAm4IM9/FXi6FPtvYHpe7wpgSaXeUcADud5lwGOl2CHA/fk1XpmXuznH9gJ+B3QA1+d13Fzqn47cP3tUyl1D+j7Kg8CPgG0q8aKPZgCT8/TNlfflktzWcrkrgCdyO6YD+1XiAr6R35tZpG/g31zpo+nAU8DiUmxU7oPpwK9z391c0z/L8vs5nXx5IbArcDvwR2Bpjhexj+W6Xs/rrJa9CHi49J6Vy/5T7p8Vud4HqVzSSPp8RaXceaSr/abnsnPK68zL/ENu76vAM6WyPymVW0H6rBWxfYF7cvy1/N6XX8s7gf/Jr/ep0nvwV6U+mp3XV46V++iO3B9FrOifGcDNwI2VeNFHM3O9HUWs9Fq/nPvosVK5oo9mkj4H88rlcv8U63mkss6ij2aS/p9eLcWKPir+9+eUYkX/zARuAnbq4nZqH9Z8fqcDLwGfr/TRz4D+jW4v273B7ukHaaPyhjy9FWmDeADwLmA4MJf0ZZRy7IiiHHAtcFoptlOp3u8B48tlc2xkLresUu8VpO9/1LXnFNIGfMcce1O5ztI6fw6cVCn7KPD23N7PAJNy7K/zP8dbc/nb8ge82DheDxyXp39LSqRFrOifOcBXgR+XYkX/KL/OyZX4TqU2300p8ZT65yrShqhc7grgo6XlzqjEiz7qk2M/pZJ48nK/J/2zFuUeBd6epycDj5M2SH0q/bMY+Fylrm/m93gOcD5wYSn2dtI/9t2kjebulbKHkS4MmUNKiOWyxedoDnAW8INK2aGkDfi8cr2kjd+XSmWr6/wg8MsiBuxR0z9zSLe5Oac07zbg8Dz9DPCbSpn7gA+QPluXkzbeWwP9S300Kb8nF5ZiRR8tBP4p11XEDgP65Xkzgf+sxIs+mkT6nP2giJX6aAHwfH6tRbnzgC/lcqdW6iz6Z5sc/0I5Xnq9k0gX0JxTKnsbcHiOfTe/70XsPuADuewnitfazW1W39xfe1b66MLyZ6iJxxY3xBTJsvx0q/yIiHggIuaQ9j6qsVtL5e4FhpViL5Wq75fLry6b7zF1EWkDtla9pTb9SXuATwPnR8TSHFtcLQfsSPon/XmlbJD+mZYBO5P+wbciHcGsiIhHJQ0h7ekJQJJIe8+Tc2yrIpbbWPRPX9L9sn5YihX9E6Q9sHdX4i/ldQwB9s59SJ5X9M/Fue7V5cpy2SMr8U+TNtJvyrHv15R7G/AO0pHG6iYBO+U69yUlD4Ddiv7Jz18BjqpUOZq0QYC0d3lM6XXOioh1frM/Im6LiJX56VTSd32KWPlztD1rv8+Q+ueFmvmd+TTpSLRYz7PrWO4Y0kZ39aLATnm6D2kDVfZWUqI/iLTR/EhErIiIxaQ+uiHHTgeOKWIRMSvXtTPpCIFS7LZIVzPuTDpKfaESfynHDiLtQUdpnZB20CAdgVGJbZvLTazEiv4p4t+pli2t8x3AtaVYAANz7B7gqVLsrcCv8rpvBz6yjn5vxShgdkTMrXyG7qH0GWpEk9mntz5IG6LppD36CyuxOaS9l7rYNqRhpuWsvfd3OWkjfBdpb3V1WeBzwBfyOldVYleQNqgzgGcrsedJh8tTSYeXL9e05yTSHvD0Stn35/LzSYfEy0h7GyIdIY3M5a5lzd7z7qR7YZFjR5CGd6pDQS+TPrAH18S2Al4ExlbjuY9eJe1Z/S1r9uaL/pmc+/Vg1j6CKPrnUdLRUTle9NELwG+Av69p072kPcRyuaJ/lufXf0Tug9X9k5dbQkoS04Bxed7i/PcJ0lDUyiJWWufdpD3Z+8tlS/EnSAn/iXKMlMRW5nX+vrTO0aQ91CdIR1nTS7HzSJ/ZGaQN4+8r7Z0OfC33/VLSEEi1PU/l97Vc7u3Ak6QjlpWkIa9y/Lf5fbs3P1aRkvcO+bXtm+dfkcv/ENghl92X9Jm+iTRkuDpWir9I2sA+UCn7w9wHL5L+T4t1jiYNdd5L+rzPKMXOy69xOWnoqRwr+mfmutqU2zOLdIuLB0pl304a+n0t99+DpdhvSYkR0s7h0g3YXv0IOL1m/k3ACU1uK7e4IwiAiFgVEfuSsu97Jf15ZZEPriN2Kek65DeVYxFxSp43i7QHUpQ9iDTm+r2IWEX6xy/XexbwNuA9wH+Shh2K2DbAqxExEjiZ9I9fbc/xpD2a6mv5AnBERAwhDQfdQLoZ4p+RvoA4ibSRnE0aC15N0lGkZDWz2m85tiq3pc5NwJMRMbEm9lNSkriP1L9IelPun9l5na9XyhT9c06OHVaJb0M6b3Id8C/AmTXtHQhcVin3BdLG+IocOw3S7iipfy6WVGzcHiENI5yW38/CgRGxH2ljVI1BGsrYbx1lryftTOxfjkXEl0nDCOeThi+K2Nm5Dw4kbZCOK8UuA95C2oj9iLQRL6+zH+lI8S2kxL59TXt+mesvl/s0abhlaO6fhZX4J4CPkz6700lJ4WXS0BJ5vfvl9i2tie0ITI6Id1VikO61tjPwf2riPyDtbF1L+ly/TEoAZ5P+N/cjbegPKZW7jHSEtDXpnNPUUqzon1Ny37w711Ft7z7ANZX2fJo1R77fyH1UxD4BfEYCMwYhAAAFPUlEQVTStPxaV9AN+UvDRwP/UZn/ZVLivaY79basyeyzKTxI/xhfKj2fQx7HLceAc0lDOX3qyuV5B7FmL/WcXGZhrnMOaSPXsY6yB5P2Ys8hjZc+DOyVYyLtzZbbsztpL3jbymv5P6TD0WLeMNIdcctl/5l0dLGQlLSWkz5oz5EOt+ezZs9oOXB1qdxK0p7lwkrsXNJe/vz8Wqvxfy7V+2qOvZiXW5zrjfx3dblS2UV5/up6cx/9a2mdr1fW+R1SQptbKncLKSEV7ZlXt85c/jDg+jx9Xn5fHgEG5XmD8vPzWPszdDf5KKRcNk+fTBrS2r4aq7xnD+bYV0nJc05+FP3/rZpyw4EHK+39BfDB0jKzSecIivb0Ix39DqmUW8Ka70kJeKnmtbwxt+mtpD339+f+fQT4yxwr+uj9wC2lcq+y5kitHDuZtAGfW2pzteycUh+9n3Sy+9nSe1n00eiacsNL5W4p+qcUnw0MqKxzMOlzNKTcntxHRTmREtPqcqX2vxW4t5vbp9HAbZV5J1P6DDX52OKOICQNkNQ/T29HGk9/uIiRL/0txySdShrj/lREvF6KPSJp71LZj+Xli/i0iHgjaS9rX9JG6C9K9Q4qteeY3I6iPT8H/i7HPkA6NF7dVtLJ7dtJY6fl9s4Cdpa0fy57KOkftFjnHhFxFmmP8g+kPa87I+LvSXu10yMdedxI2vjeGREnAORy80l7WMcVsdw/fwu8MyKGRMTwIg6cKGnvXHYoKRHdmMvuEhFvjIj+EdGPtPf1N6V6B+XXenYud0l5vbmPpub2nkxKUKvbm/vq6ojYs9Se0aS908tzufNIw1PFOvfI/blLXu8PJO1AShYPkm7/cqqkHYExwK2lWKEPaW+UcllJHyId5RwfEcsrsRGSdsj1js7v92HAfRGxB+no7y9y/x9IuuDgwaKPcl3H5Xnl9v4cOEzSjpLeSjrqOrDU3iOBxyJifqXcU8AH8rwjgccq7d0jIhaSNsrfJO3ZjyLtjEwhDdvNA76Y3+8iRi73KuloiSKW++cfSUcqT0rapxIfUVrnJ/P7Owq4PyL2iHS08z+knYH9SBdWPCRpUKncuPz6ivb8nJRAF5J2kLbPf1e3N/f7UtLQEaXYU6Qj3Hmk4d7HSm0tPkd9gK/k/umO4ymdGyr10dERsbybdbau6QzU2x6kPZsHSOOQD5Kv3AA+S9qTCtIlgS+UYitJH4LlpD3uZ0h75H1IG5eZpA/HC7nO1fVW1rmqss47c7lXSHvTD5Vi/UljsK+QNpwdlTrvJh3i1r2WD5fqXUZKEEXsItZczvd51h6bfzNpT7CDdEh7aCn2WdLGaSXpH+OWUmwlac+ruCTvHNYcEZX76EHShv4I6q82WlZpz52lcleTrsoqx/vndswkbRjGsvZ5j7tJt5CnUu7Duczv8zLHl2JF/zxOOo9QXA795RzfLb+e10gbjYdLsQ/nPnqN9Bl6qVK2I/fdK/nxQin20/yevELaM32kiJXem+Ky5vI6r8qv5WHWXO5cXufWpI1gcaQ4p1Lv5Nzm6us8kDRcNYv0+Xu0Ev9cnjeXdFQ4I69nl9xHd+RY0QdFrOijFay5VLiIdZD+z6bn1/9spd6fkj4Lj5KOOosN/C6l17Nv7v/yOos++pNyuX+uzvUW/xczyvWShhq/TjqyKben6KNHWHM5eREr+udR0lG5urGt2oE0SrBzaV65j6ZTudptYz98qw0zM6u1xQ0xmZlZa5wgzMyslhOEmZnVcoIwM7NaThBmZlbLCcLMzGo5QZiZWa3/D5bv1UeBUoXQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, p = 100, 0.5\n",
    "samples = np.random.binomial(n, p, size=10000)\n",
    "\n",
    "unique, counts = np.unique(samples, return_counts=True)\n",
    "\n",
    "plt.bar(unique, counts)\n",
    "plt.xticks(unique, unique)\n",
    "plt.ylabel('Ocurrencias')\n",
    "plt.title('Distribución Binomial')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media estimada: 50.0014, Teórica: 50.0\n",
      "Varianza estimada: 24.94659804, Teórica: 25.0\n"
     ]
    }
   ],
   "source": [
    "print('Media estimada: {}, Teórica: {}'.format(np.mean(samples), n*p))\n",
    "print('Varianza estimada: {}, Teórica: {}'.format(np.std(samples)**2, n*p*(1-p)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribución Uniforme Continua:\n",
    "\n",
    "El PDF de una distribución uniforme continua está dado por:\n",
    "\n",
    "$$ f_{X}(x)=   \\left\\{\n",
    "\\begin{array}{ll}\n",
    "      0 & x < a \\\\\n",
    "      \\frac{1}{b-a} & x \\in [a,b] \\\\\n",
    "      1 & x > b \\\\\n",
    "\\end{array} \n",
    "\\right.  $$\n",
    "\n",
    "$\\mathbb{E}(X) = \\int^{b}_{a}x\\dfrac{1}{b-a}dx = \\dfrac{x^{2}}{2(b-a)}\\Big|_{a}^{b} = \\dfrac{(b+a)(b-a)}{2(b-a)} = \\dfrac{(b+a)}{2}$\n",
    "\n",
    "Para calcular la varianza:\n",
    "$\\mathbb{E}(X^{2}) = \\int^{b}_{a}x^{2}\\dfrac{1}{b-a}dx = \\dfrac{x^{3}}{3(b-a)}\\Big|_{a}^{b} = \\dfrac{b^{3}-a^{3}}{3(b-a)} = \\dfrac{(b-a)(b^{2}+2ab+a^{2})}{3(b-a)} = \\dfrac{b^{2}+ab+a^{2}}{3}$\n",
    "\n",
    "$var(x) = \\dfrac{b^{2}+ab+a^{2}}{3} - \\Big(\\dfrac{(b+a)}{2}\\Big)^{2} = \\dfrac{b^{2}+ab+a^{2}}{3} - \\dfrac{b^{2}+2ab+a^{2}}{4} = \\dfrac{4(b^{2}+ab+a^{2})-3(b^{2}+2ab+a^{2})}{12} = \\dfrac{(b-a)^{2}}{12}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Distribución uniforme')"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0\n",
    "b = 20\n",
    "samples = np.random.uniform(low=a, high=b, size=10000000)\n",
    "\n",
    "unique, counts = np.unique(samples, return_counts=True)\n",
    "\n",
    "plt.hist(samples, bins = 100)\n",
    "plt.ylabel('Ocurrencias')\n",
    "plt.title('Distribución uniforme')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media estimada: 9.999352405259122, Teórica: 10.0\n",
      "Varianza estimada: 33.33466207709399, Teórica: 33.333333333333336\n"
     ]
    }
   ],
   "source": [
    "print('Media estimada: {}, Teórica: {}'.format(np.mean(samples), (a+b)/2))\n",
    "print('Varianza estimada: {}, Teórica: {}'.format(np.std(samples)**2, (b-a)**2/12))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribución Normal:\n",
    "\n",
    "El PDF de una distribución Normal está dado por:\n",
    "\n",
    "$$ f_{X}(x)= \\dfrac{1}{\\sigma\\sqrt{2\\pi}}\\exp{-\\dfrac{(x-\\mu)^{2}}{2\\sigma^{2}}}, x \\in \\mathcal{R}$$\n",
    "\n",
    "$\\textbf{Obs}$: $\\mu$ y $\\sigma$ son definidos como el centro (media) y la dispersión (varianza) de la distribución. Cuando una distribución normal tiene $\\mu = 0$ y $\\sigma=1$, esta es llamada distrbución normal estándar, cuyo PDF está deotado por $\\phi(z)$ y CDF $\\Phi(z)$. \n",
    "\n",
    "$\\textbf{Propiedades útiles}$:\n",
    "\n",
    "1.- Si $X \\sim \\mathcal{N}(\\mu, \\sigma^{2})$, entonces $Z = \\dfrac{X-\\mu}{\\sigma} \\sim \\mathcal{N}(0,1)$.\n",
    "\n",
    "2.- Además, podemos calcular la probabilidad de la distribución sobre un intervalo de la siguiente forma:\n",
    "$$P(a<X<b) = P \\Big(\\dfrac{a-\\mu}{\\sigma}<Z<\\dfrac{b-\\mu}{\\sigma}\\Big) = \\phi\\Big(\\dfrac{b-\\mu}{\\sigma}\\Big) - \\phi\\Big(\\dfrac{a-\\mu}{\\sigma}\\Big)$$\n",
    "Donde los valores de cualquier $\\phi(z)$ son conocidos.\n",
    "\n",
    "$\\mathbb{E}(X) = \\mu$\n",
    "\n",
    "$var(X) = \\sigma^{2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Distribución normal')"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu, sigma = 0, 1\n",
    "\n",
    "samples = np.random.normal(loc=mu, scale=sigma, size=100000)\n",
    "\n",
    "plt.hist(samples, bins=100)\n",
    "plt.ylabel('Ocurrencias')\n",
    "plt.title('Distribución normal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media estimada: -0.0005145390573908088, Teórica: 0\n",
      "Varianza estimada: 0.9956133976717266, Teórica: 1\n"
     ]
    }
   ],
   "source": [
    "print('Media estimada: {}, Teórica: {}'.format(np.mean(samples), mu))\n",
    "print('Varianza estimada: {}, Teórica: {}'.format(np.std(samples)**2, sigma))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Teorema del Límite Central\n",
    "\n",
    "Sea $X_{1}, X_{2}, ...n X_{n}$ muestras i.i.d con media $\\mu$ y varianza $\\sigma^{2}$. Sea $\\bar{X}_{n}=\\dfrac{1}{n}\\sum_{i=1}^{n}X_{i}$, entonces:\n",
    "\n",
    "$$ Z_{n}=\\dfrac{\\sqrt{n}(\\bar{X}_{n}-\\mu)}{\\sigma} \\rightarrow Z \\sim \\mathcal{N}(0,1)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Teorema del limite central')"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEICAYAAABI7RO5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAHiZJREFUeJzt3XucHWWd5/HPNxcuA0gSEjEkgUQNg6gzAVvAK0gEA+tyWRXCigaGMSAwqzu6M0GdRXGZRRR4yYLRCJHgqiEqSpQghtsiaiDJGAMJYpoAJjEkzS0SUTT42z/q6Vg0falKTp1T3f19v1716qqnnqrzO+d09+88l6qjiMDMzKyoIa0OwMzM+hcnDjMzK8WJw8zMSnHiMDOzUpw4zMysFCcOMzMrxYnDrCBJB0naVrDuOZJuK3IeSXdIOnUHY7pO0r/syLH9iaRLJF3T6jgs48RhpUnamlv+IukPue33tzq+/iYijo6IG3bw2DMi4lIASdMktTc2up0naYmk01sdhzXOsFYHYP1PROzZuS7pUeAfI6LbT9c7Q9KwiCj0Cd/6L7/P/Y9bHNZwkoZK+jdJayU9Iekbkkbk9r9H0mpJz0i6TdLk3L7HJX1c0irgd6lsgqSb0rnWSjonV/+SdP4bUotnhaRJki5M9R+V9I5c/bMl/UrSs5LaJf1DL89jmKQvSnoyfZI/psv+UZKuTzGvS49Z+m8q/4k8dXHdIekqSVskrZHUJmmmpA2SNkmanjt2vqRPSdoH+B7wylzrb5++3otuYnmfpJXp9VkjaWpfzzXFfLukK9N7+rCkd6Z9lwFvBK5JMV0maTdJIenDkh4GHkh1Z0taL+l3ku6TdETZ19Kaw4nDqvBx4FjgrcB44M/AFQCSXg9cB5wLvBz4f8BNkvKt31PJ/knvI2kosAj4GbAfMA34hKQjc/VPBr4MjAAeAu4Afg+8ArgM+FKu7kbgOOBlwDnA1ZJe28PzOB84Gng98KYUV943gC3AK4HDgJOAD/T2whT0NrLnOwr4PvBd4DXAJOBDwGxJu+UPiIgnyV6HtRGxZ1qepJf3oitJbwfmAB8B9gamAusKPte3A8uAfYCrgGtSXB8DlpK1SvdM253eDbwBOCRt/5zstd4HuAn4tqThfb9c1nQR4cXLDi/Ao8A7u5Q9Arwltz0JeA4QcDFwfW7fUKADOCJtPw7819z+I4E1Xc7/GWB2Wr8E+EFu3/uAJwGl7TFAALv3EP+PgLN72Pcz4Izc9gnAtrR+AFlyGp7bfyZwS1o/B7ith/Me1HmetL0EOD133P25fW9M8e+dK/s9cFBanw98Kq1PA9qLvhfdxDUP+N/dlBd5rg/k9o1KMY/o+vzS9m5p/5t7+b1SivNvc+/zNa3+ffeSLR7jsIaSJGACsEhS/g6aQ8g+Se4HPNZZGBEvSNoAjMvVXZdbPwCYKOmZXNlQID+msim3/gegI9J/m7QNsAfwB0knAJ8CXp1i+hvgJz08nf26xPJYbv0Asn+AHdlT3v4cGzE43fX5PB8RW7qU7UkfCrwXT3Q5ZALdvxZFnuvjufXn0s89gfz71lX+tUXSBcAZZC3FSI85mqwVaTXixGENFRGREsF/iYjlXfdL+i3ZP6LO7aFkSWND/jS59XXAryLi9Tsbm6Q9gG8D7yX7tLxN0o/IPt12ZyPZP9NO+3eJayswMpekWu1FcfT1XnRjHfCqHsp35rn2dMz2cknHAP8EvBN4kOw9eZae3xtrIY9xWBW+DFwiaQKApJdL+s9p3w3AyZLenvqvZ5F1LS3r4Vz3pHN8NA2qDpP0d5IO3YG4dgeGA5uBv6TWx1G91F8A/HdJYyWNBrZfLxERj5B1wVwqaS9JQyRNlvTWHYirUTYBL5eUb4309l50dQ1wdnpvhiiblHBgA57rJrKxkd7sRTb+0gHsAlxE1uKwGnLisCpcStaVdIekZ8nGCg4FiIiVwFnAV8j+SUwFTowepmNGxJ+B44E3k3UVdQCzKdBV0825niAbLP4BWbI6iWzgvSdXkXXdrALuJUskeaeRDcj/CniKLCnuWzauBvolsBB4LM1uGkUv70VXEfETsvGKL5ENhN9ONqAOO/dcrwA+KOlpSZf2UOcHwN3Aw8Basm60joLntyZTfVrZZmbWH7jFYWZmpThxmJlZKU4cZmZWihOHmZmVMiCv4xg9enRMnDix1WGYmfUry5cvfyIixvRVb0AmjokTJ7JsWU+XBZiZWXckPdZ3LXdVmZlZSU4cZmZWihOHmZmV4sRhZmalOHGYmVkpThxmZlaKE4eZmZXixGFmZqU4cZiZWSkD8spxs1aZOOvm7euPXvKfWhiJWXXc4jAzs1KcOMzMrJTKEoek3STdJ+mXklZJ+kwqv07SI5JWpGVKKpekKyW1S1op6dDcuWZIWpOWGVXFbGZmfatyjON54OiI2CppOHCPpFvSvv8REd/pUv84YHJaDgdmA4dLGgVcCLQBASyXtDAinq4wdrOd5vEOG6gqa3FEZmvaHJ6W6OWQE4Hr03FLgBGSxgLvAhZHxFMpWSwGplUVt5mZ9a7SMQ5JQyWtADaT/fO/N+26OHVHXSFp11Q2DliXO3x9Kuup3KxlJs66eftiNthUmjgi4oWImAKMBw6T9DrgAuAg4I3AKOBfG/FYkmZKWiZpWUdHRyNOaWZm3WjKdRwR8YykO4FpEfGFVPy8pK8BH0/bG4AJucPGp7INwFFdyu/q5jHmAHMA2traeusSM2sotzpssKkscUgaA/w5JY3dgWOAz0kaGxEbJQk4CXggHbIQOF/SfLLB8S2p3q3Av0sameodS9ZqMWsqJwizTJUtjrHAPElDybrEFkTEDyXdkZKKgBXAOan+IuB4oB14DjgTICKekvRZYGmqd1FEPFVh3GZm1ovKEkdErAQO6ab86B7qB3BeD/vmAnMbGqBZi3iarvV3vleVWS8a1T3lbi4bSHzLETMzK8WJw8zMSnFXlVkLebzD+iO3OMzMrBQnDjMzK8WJw8zMSnHiMDOzUpw4zMysFCcOMzMrxYnDzMxKceIwM7NSfAGgDXpd7yPlC/HMeucWh5mZleLEYWZmpbiryqwmfN8q6y/c4jAzs1Lc4jDrwl+6ZNY7tzjMzKwUJw4zMyulssQhaTdJ90n6paRVkj6TyidJuldSu6QbJO2SyndN2+1p/8TcuS5I5Q9JeldVMZuZWd+qHON4Hjg6IrZKGg7cI+kW4J+BKyJivqQvA2cBs9PPpyPi1ZKmA58DTpV0MDAdeC2wH3CbpAMj4oUKY7cBru7jGJ5hZXVWWYsjMlvT5vC0BHA08J1UPg84Ka2fmLZJ+6dKUiqfHxHPR8QjQDtwWFVxm5lZ7yod45A0VNIKYDOwGHgYeCYitqUq64FxaX0csA4g7d8C7JMv7+aY/GPNlLRM0rKOjo4qno6ZmVFx4oiIFyJiCjCerJVwUIWPNSci2iKibcyYMVU9jJnZoNeUWVUR8QxwJ/AmYISkzrGV8cCGtL4BmACQ9u8NPJkv7+YYMzNrsipnVY2RNCKt7w4cAzxIlkDem6rNAG5K6wvTNmn/HRERqXx6mnU1CZgM3FdV3GZ1M3HWzdsXszqoclbVWGCepKFkCWpBRPxQ0mpgvqT/BfwCuDbVvxb4uqR24CmymVRExCpJC4DVwDbgPM+oMjNrncoSR0SsBA7ppnwt3cyKiog/Au/r4VwXAxc3OkYzMyvPV46bmVkpThxmZlaKE4eZmZXixGFmZqU4cZiZWSlOHGZmVooTh5mZleLEYWZmpThxmJlZKU4cZmZWihOHmZmVUuVNDs1qxXeXNWsMJw6zfsTfRW514K4qMzMrxYnDzMxKcVeVDWge1zBrPLc4zMysFCcOMzMrxYnDzMxKceIwM7NSKksckiZIulPSakmrJH0klX9a0gZJK9JyfO6YCyS1S3pI0rty5dNSWbukWVXFbGZmfatyVtU24GMR8R+S9gKWS1qc9l0REV/IV5Z0MDAdeC2wH3CbpAPT7quBY4D1wFJJCyNidYWxm5lZDypLHBGxEdiY1p+V9CAwrpdDTgTmR8TzwCOS2oHD0r72iFgLIGl+quvEYWbWAk0Z45A0ETgEuDcVnS9ppaS5kkamsnHAutxh61NZT+VdH2OmpGWSlnV0dDT4GZiZWafKE4ekPYHvAh+NiN8Bs4FXAVPIWiSXNeJxImJORLRFRNuYMWMacUozM+tGpVeOSxpOljS+ERE3AkTEptz+rwI/TJsbgAm5w8enMnopNxu0fMNDa5UqZ1UJuBZ4MCIuz5WPzVU7GXggrS8EpkvaVdIkYDJwH7AUmCxpkqRdyAbQF1YVt5mZ9a7KFsdbgA8A90takco+AZwmaQoQwKPA2QARsUrSArJB723AeRHxAoCk84FbgaHA3IhYVWHc1s/5/lRm1apyVtU9gLrZtaiXYy4GLu6mfFFvx5mZWfP4ynEzMyulUOKQ9BZJe6T10yVdLumAakMzM7M6KtrimA08J+nvgY8BDwPXVxaVmZnVVtHEsS0iguyK7asi4mpgr+rCMjOzuio6OP6spAuA04G3SxoCDK8uLDMzq6uiLY5TgeeBsyLicbKL8D5fWVRmZlZbhVocKVlcntv+DR7jMDMblAolDklHAP8HeA2wC9mFeFsjYu8KYzOzgnz7EWumol1VVwGnAWuA3YF/BL5UVVBmZlZfha8cj4h2SUPTbUC+JukXwAXVhWZWnG8zYtY8RRPHc+kGgyskXUp2O3RfdW5mNggV/ef/AbJxjfOB35Pd5vw9VQVlZmb1VXRW1WNp9Q/AZ6oLx8zM6q7XxCFpQUScIul+stugv0hE/F1lkZnZDvEMK6taXy2Oj6Sf7646EDMz6x96TRwRsTGtDgE2RsQfASTtDuxbcWxmZlZDRQfHvw38Jbf9QiozM7NBpmjiGBYRf+rcSOu7VBOSmZnVWdHE0SHphM4NSScCT1QTkpmZ1VnRxHEO8AlJv5G0DvhX4OzeDpA0QdKdklZLWiXpI6l8lKTFktaknyNTuSRdKald0kpJh+bONSPVXyNpxo49VTMza4Si13E8DBwhac+0vbXAYduAj0XEf0jaC1guaTFwBnB7RFwiaRYwiywRHQdMTsvhZN86eLikUcCFQBvZlODlkhZGxNMlnqeZmTVI0bvj7kp2pfhEYJgkACLiop6OSTOyNqb1ZyU9CIwj+xbBo1K1ecBdZInjROD69E2DSySNkDQ21V0cEU+lWBYD04BvFX+aNhD5/lRmrVH0XlU3AVuA5WRf6FSKpInAIcC9wL65ab6P89dpveOAdbnD1qeynsq7PsZMYCbA/vvvXzZEMzMrqGjiGB8R03bkAVL31neBj0bE7zpbKwAREZJeckX6joiIOcAcgLa2toac06y/81XkVoWig+M/k/T6sieXNJwsaXwjIm5MxZtSFxTp5+ZUvoHs5omdxqeynsrNzKwFiiaOt5INSj+UZjzdL2llbwcoa1pcCzwYEZfndi0EOmdGzSDrBuss/2CaXXUEsCV1ad0KHCtpZJqBdWwqMzOzFijaVXXcDpz7LWS3Y79f0opU9gngEmCBpLOAx4BT0r5FwPFAO/AccCZARDwl6bPA0lTvos6BcjMza77Ct1WX9FZgckR8TdIYYM8+jrkHUA+7p3ZTP4DzejjXXGBukVjNzKxahbqqJF1INmW286tihwP/t6qgzMysvoqOcZwMnED27X9ExG+BvaoKyszM6qvoGMef8lNnJe1RYUxmPfJFf2atV7TFsUDSV4ARkj4E3AZ8tbqwzMysrooOjn9B0jHA74C/Bf5nRCyuNDIzM6ulPhOHpKHAbRHxDsDJwsxskOszcUTEC5L+ImnviNjSjKDMrPF8+xFrlKKD41vJLuRbTJpZBRAR/62SqMzMrLaKJo4b02JmZoNc0TGOYyPi/U2Ix8zMaq7P6bgR8QJwgKRdmhCPmZnVXNGuqrXATyUt5MVjHJf3fIiZmQ1ERRPHw2kZgm81Yk3mq8XN6qXoBYCfqToQMzPrHwolDkl3Ai/5OtaIOLrhEZmZWa0V7ar6eG59N+A9wLbGh2NmZnVXtKtqeZein0q6r4J4zMys5op2VY3KbQ4B3gDsXUlEZlY5337EdkbRrqrlZGMcIuuiegQ4q6qgzMysvop2VU2qOhAzM+sfin7n+HmSRuS2R0o6t49j5kraLOmBXNmnJW2QtCItx+f2XSCpXdJDkt6VK5+WytolzSr39MzMrNGKfgPghyLimc6NiHga+FAfx1wHTOum/IqImJKWRQCSDgamA69Nx3xJ0tB0n6yrgeOAg4HTUl0zM2uRomMcQyUpIjq/c3wo0Ou9qyLibkkTC57/RGB+RDwPPCKpHTgs7WuPiLXpceenuqsLntf6KV8tblZfRVsctwI3SJoqaSowH/jRDj7m+ZJWpq6skalsHLAuV2d9Kuup/CUkzZS0TNKyjo6OHQzNzMz6UjRx/BtwD3BuWhYD/7IDjzcbeBUwBdgIXLYD5+hWRMyJiLaIaBszZkyjTmtmZl302lUlaRjw78CZ/PWT//5kd8sdArxQ5sEiYlPu3F8Ffpg2NwATclXHpzJ6KTczsxboq8XxeWAU8MqIODQiDgUmkV3894WyDyZpbG7zZKBzxtVCYLqkXSVNAiYD9wFLgcmSJqXvA5me6pqZWYv0NTj+buDAzkFxgIh4VtKHgV8BH+npQEnfAo4CRktaD1wIHCVpCtnFhI8CZ6dzrpK0gGzQextwXvoCKSSdTzbGMhSYGxGrduB5mlkPfBW5ldVX4oh80sgVviDpJeVd6pzWTfG1vdS/GLi4m/JFwKI+4jQzsybpK3GslvTBiLg+XyjpdLIWh1nDeAquWf/QV+I4D7hR0j+Q3a8KoA3YnWyMwszMBpleE0dEbAAOl3Q02VXdAIsi4vbKIzMzs1oqepPDO4A7Ko7FzMz6gaIXAJqZmQFOHGZmVpITh5mZleLEYWZmpRS9rbqZDQK+ityKcIvDzMxKceIwM7NSnDjMzKwUJw4zMyvFicPMzErxrCprKd8Rt766vjeeZWWd3OIwM7NSnDjMzKwUJw4zMyvFicPMzEqpLHFImitps6QHcmWjJC2WtCb9HJnKJelKSe2SVko6NHfMjFR/jaQZVcVrZmbFVNniuA6Y1qVsFnB7REwGbk/bAMcBk9MyE5gNWaIBLgQOBw4DLuxMNmZm1hqVJY6IuBt4qkvxicC8tD4POClXfn1klgAjJI0F3gUsjoinIuJpYDEvTUZmZtZEzR7j2DciNqb1x4F90/o4YF2u3vpU1lO5mZm1SMsGxyMigGjU+STNlLRM0rKOjo5GndbMzLpo9pXjmySNjYiNqStqcyrfAEzI1RufyjYAR3Upv6u7E0fEHGAOQFtbW8MSkjWerxY369+a3eJYCHTOjJoB3JQr/2CaXXUEsCV1ad0KHCtpZBoUPzaVmVmTTZx18/bFBrfKWhySvkXWWhgtaT3Z7KhLgAWSzgIeA05J1RcBxwPtwHPAmQAR8ZSkzwJLU72LIqLrgLuZmTVRZYkjIk7rYdfUbuoGcF4P55kLzG1gaNYC/pRqNnD4ynEzMyvFicPMzEpx4jAzs1KcOMzMrBR/A6CZlZaf7OBvBhx83OIwM7NSnDjMzKwUJw4zMyvFicPMzErx4LhVxleLmw1MbnGYmVkpThxmZlaKE4eZmZXiMQ4z2ym+GHDwcYvDzMxKceIwM7NSnDjMzKwUj3FYQ/naDbOBz4nDdpqThXXyQPng4K4qMzMrpSWJQ9Kjku6XtELSslQ2StJiSWvSz5GpXJKulNQuaaWkQ1sRs5mZZVrZ4nhHREyJiLa0PQu4PSImA7enbYDjgMlpmQnMbnqkZma2XZ26qk4E5qX1ecBJufLrI7MEGCFpbCsCNDOz1iWOAH4sabmkmals34jYmNYfB/ZN6+OAdblj16eyF5E0U9IyScs6OjqqitvMbNBr1ayqt0bEBkkvBxZL+lV+Z0SEpChzwoiYA8wBaGtrK3WsmTWeZ1gNXC1pcUTEhvRzM/A94DBgU2cXVPq5OVXfAEzIHT4+lZmZWQs0vcUhaQ9gSEQ8m9aPBS4CFgIzgEvSz5vSIQuB8yXNBw4HtuS6tKxFfO2G2eDViq6qfYHvSep8/G9GxI8kLQUWSDoLeAw4JdVfBBwPtAPPAWc2P2QzM+vU9MQREWuBv++m/ElgajflAZzXhNDMrCIe7xhY6jQd18zM+gEnDjMzK8U3ObTCPCBuZuDEYWZN5vGO/s9dVWZmVooTh5mZleKuKuuVxzXMrCsnDjNrGY939E9OHPYSbmWYWW88xmFmZqW4xWGAWxnWeu626j/c4jAzs1KcOMzMrBR3VQ1S7pqyOnO3Vb05cQwiThZm1ghOHGZWaz194HFLpHU8xmFmZqW4xTHAuXvKzBrNiWMAcrKwwcBdWK3jxDFAOFmYZTwjq3r9JnFImgZ8ERgKXBMRl7Q4pJZzsjDrnZNINfpF4pA0FLgaOAZYDyyVtDAiVrc2suo4KZg1lru2GqdfJA7gMKA9ItYCSJoPnAjULnEU+YTjpGBWH0USilsuL9ZfEsc4YF1uez1weL6CpJnAzLS5VdJDwGjgiaZE2A19rtfdLY2tgDrHV+fYoN7x1Tk2qFF83fz9jgae6OPvupUa8dodUKRSf0kcfYqIOcCcfJmkZRHR1qKQelXn2KDe8dU5Nqh3fHWODeodX51jg+bG118uANwATMhtj09lZmbWZP0lcSwFJkuaJGkXYDqwsMUxmZkNSv2iqyoitkk6H7iVbDru3IhYVeDQOX1XaZk6xwb1jq/OsUG946tzbFDv+OocGzQxPkVEsx7LzMwGgP7SVWVmZjXhxGFmZqUMqMQhaZSkxZLWpJ8je6h3qaRVkh6UdKUk1Si2/SX9OMW2WtLEqmMrE1+q+zJJ6yVdVZfYJE2R9PP0vq6UdGrFMU2T9JCkdkmzutm/q6Qb0v57m/U+lojvn9Pv10pJt0sqNH+/GbHl6r1HUkhq6hTYIvFJOiW9fqskfbMusaX/H3dK+kV6b4+vJJCIGDALcCkwK63PAj7XTZ03Az8lG2QfCvwcOKoOsaV9dwHHpPU9gb+py2uXq/tF4JvAVXWJDTgQmJzW9wM2AiMqimco8DDwSmAX4JfAwV3qnAt8Oa1PB25oxmtVIr53dP5uAR9uVnxFYkv19gLuBpYAbTV77SYDvwBGpu2X1yi2OcCH0/rBwKNVxDKgWhxktyGZl9bnASd1UyeA3che+F2B4cCmOsQm6WBgWEQsBoiIrRHxXBNiKxQfgKQ3APsCP25SXFAgtoj4dUSsSeu/BTYDYyqKZ/stcCLiT0DnLXB6ivk7wNRmtGyLxhcRd+Z+t5aQXRtVi9iSzwKfA/7YpLg6FYnvQ8DVEfE0QERsrlFsAbwsre8N/LaKQAZa4tg3Ijam9cfJ/sG9SET8HLiT7BPpRuDWiHiwDrGRfWp+RtKNqan5+XSDx2boMz5JQ4DLgI83KaZORV677SQdRvbB4OGK4unuFjjjeqoTEduALcA+FcXTVZH48s4Cbqk0or/qMzZJhwITIqIVN3Ur8todCBwo6aeSlqQ7d9cltk8Dp0taDywC/qmKQPrFdRx5km4DXtHNrk/mNyIiJL1krrGkVwOv4a+fsBZLeltE/KTVsZG9H28DDgF+A9wAnAFcu7OxNSi+c4FFEbG+0R+eGxBb53nGAl8HZkTEXxoa5AAk6XSgDTiy1bHA9g8nl5P93tfVMLLuqqPI/o/cLen1EfFMS6PKnAZcFxGXSXoT8HVJr2v030K/SxwR8c6e9knaJGlsRGxM/0C6a0KeDCyJiK3pmFuANwE7nTgaENt6YEX89S7A3weOoEGJowHxvQl4m6RzycZfdpG0NSJ6HOBsYmxIehlwM/DJiFiyszH1osgtcDrrrJc0jKzb4MkKY+rusTt1e4seSe8kS8xHRsTzNYltL+B1wF3pw8krgIWSToiIZTWID7K/03sj4s/AI5J+TZZIltYgtrOAaZD1rkjajezmhw3tThtoXVULgRlpfQZwUzd1fgMcKWmYpOFkn7Sa0VVVJLalwAhJnX3zR9O8W8f3GV9EvD8i9o+IiWTdVdc3Imk0IjZlt6L5XorpOxXHU+QWOPmY3wvcEWnEsgn6jE/SIcBXgBOa2EffZ2wRsSUiRkfExPR7tiTF2Iyk0Wd8yffJWhtIGk3WdbW2JrH9BpiaYnsN2XhuR8MjacZsgGYtZH3ItwNrgNuAUam8jexbAyGbmfAVsmSxGri8LrGl7WOAlcD9wHXALnWKL1f/DJo3q6rI+3o68GdgRW6ZUmFMxwO/JhtH+WQqu4jsnxxkf7DfBtqB+4BXNuO1KhHfbWSTQjpfq4V1ia1L3bto4qyqgq+dyLrTVqe/0+k1iu1gslmjv0zv67FVxOFbjpiZWSkDravKzMwq5sRhZmalOHGYmVkpThxmZlaKE4eZmZXixGFmZqU4cZiZWSn/H6rVdT458ZNfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0\n",
    "b = 20\n",
    "\n",
    "Z_n_samples = []\n",
    "\n",
    "for i in range(100000):\n",
    "    samples = np.random.uniform(low=a, high=b, size=1000)\n",
    "    X_bar = np.mean(samples)\n",
    "    Z_n = len(samples)**(1/2)*(X_bar-(a+b)/2)/((b-a)**2/12)\n",
    "    Z_n_samples.append(Z_n)\n",
    "\n",
    "\n",
    "plt.hist(Z_n_samples, bins = 100)\n",
    "plt.ylabel('Ocurrencias')\n",
    "plt.title('Teorema del limite central')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribución Conjunta:\n",
    "\n",
    "**Función de masa conjunta**: Dadas dos variables aleatorias $X$ e $Y$, definimos la función de masa conjunta como:\n",
    "\n",
    "$$f(x,y)=P(X=x, Y=y)$$\n",
    "\n",
    "Por ejemplo:\n",
    "\n",
    "|- | $Y=0$| $Y=1$ | $\\sum$ |\n",
    "|--| ------------- | ------------- | --|\n",
    "|$X=0$| $\\frac{1}{9}$  | $\\frac{2}{9}$  | $\\frac{1}{3}$|\n",
    "|$X=1$| $\\frac{2}{9}$  | $\\frac{4}{9}$  | $\\frac{2}{3}$|\n",
    "|$\\sum$| $\\frac{1}{3}$  | $\\frac{2}{3}$  | $1$|\n",
    "\n",
    "\n",
    "**Obs**: Para poder calcular distribuciones conjuntas tenemos que:\n",
    "\n",
    "1. Diseñar una tabla listando todas las combinaciones de variables.\n",
    "2. Para cada combinación, qué tan probable es ésta.\n",
    "3. Las probabilidades deben sumar 1.\n",
    "\n",
    "A través de las distribuciones conjuntas podemos responder a cualquier expresion logica que envuelva esas variables.\n",
    "\n",
    "$$P(Y=1|X=0) = \\dfrac{P(X=0,Y=1)}{P(X=0)} = ?$$\n",
    "\n",
    "%\\dfrac{\\frac{2}{9}}{\\frac{1}{3}} = \\dfrac{2}{3} $$\n",
    "\n",
    "\n",
    "Entonces si queremos predecir la probabilidad de alguna variable, basta con aprender las probabilidades conjuntas?\n",
    "\n",
    "1. No es fácil aprender las conjuntas. Supongamos que tenemos más atributos y que estos no son independientes.\n",
    "2. ¿Cómo crece la cantidad de probabilidades que tenemos que calcular para variables aleatorias discretas si tenemos atributos binarios?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistical Learning\n",
    "\n",
    "El aprendizaje estadistico es el proceso mediante el cual usamos datos para estimar la distribución de probabilidad que generan estos datos.\n",
    "\n",
    "Un **modelo estadístico** es un set de distribuciones (o densidades) $\\mathcal{P}$. Un **modelo paramétrico** es un set $\\mathcal{P}$ que puede ser parametrizado por un número finito de parámetros y se denota como:\n",
    "\n",
    "$$\\mathcal{P}=\\Big\\{f(x;\\theta): \\theta \\in \\Theta \\Big\\}$$\n",
    "\n",
    "Donde $\\theta$ es un parámetro desconocido (o un vector de parámetros) que puede tomar valores en el espacio de parámetros $\\Theta$\n",
    "\n",
    "Ej 1: Si asumimos que los datos provienen de una distribución Normal, entonces el modelo está definido por:\n",
    "$$\\mathcal{P} = \\Big\\{f(x;\\mu,\\sigma)=\\dfrac{1}{\\sigma \\sqrt{\\pi}}\\exp\\Big({\\dfrac{-(x-\\mu)^{2}}{2\\sigma^{2}}\\Big)}, \\mu \\in \\mathbb{R}, \\sigma >0\\Big\\}$$\n",
    "\n",
    "Ej 2: Supongamos que observamos los pares de datos $(X_{1}, Y_{1}), (X_{2}, Y_{2}), ..., (X_{n}, Y_{n})$, donde $X_{i}$ es la presión sanguinea del sujeto $i$ e $Y_{i}$ es la esperanza de vida del sujeto $i$. Podemos llamar $r(x) = \\mathbb{E}(Y|X=x) = \\theta_{0}+\\theta_{1}x$ a la función regresora. Podemos asumir que $\\mathcal{P}$ es un set finito de lineas rectas, entonces tenemos un modelo paramétrico. El objetivo de este modelo paramétrico consiste en estimar los parámetros $\\theta_{0}$ y $\\theta_{1}$.\n",
    "\n",
    "\n",
    "**Definciones**\n",
    "\n",
    "\n",
    "**Estimación puntual**: Se refiere a la mejor estimación del parámetro o densidad de interés. En un modelo paramétrico denotamos al estimador puntual del parámetro $\\theta$ como $\\hat{\\theta}$. Esta estimación $\\hat{\\theta}$ depende de los datos, que son variables aleatorias, por lo tanto es también una variable aleatoria que depende de los datos:\n",
    "\n",
    "$$\\hat{\\theta} = g(X_{1},...,X_{n})$$\n",
    "\n",
    "\n",
    "Se define el sesgo de un estimador puntual como:\n",
    "$$bias(\\hat{\\theta}_{n}) = \\mathbb{E}(\\hat{\\theta}_{n}) - \\theta$$\n",
    "\n",
    "Por lo tanto, $\\hat{\\theta}_{n}$ es no sesgado si $\\mathbb{E}(\\hat{\\theta}_{n}) = \\theta$. Podemos ver el sesgo como: Si ejecuto un experimento multiples veces y promedio su estimador puntial, debiese obtener el parámetro real.\n",
    "\n",
    "Se define como el error estándar de $\\hat{\\theta}_{n}$ como:\n",
    "$$se(\\hat{\\theta}_{n}) = \\sqrt{V(\\hat{\\theta}_{n})} = \\mathbb{E}(\\hat{\\theta}-\\mathbb{E}(\\hat{\\theta}))$$\n",
    "\n",
    "La calidad de un estimador puntual comúnmente se mide mediante el **error cuadrático medio**:\n",
    "$$MSE = \\mathbb{E}_{\\theta}(\\hat{\\theta}_{n} - \\theta )^{2} = bias(\\hat{\\theta}_{n})^{2} + V(\\hat{\\theta}_{n})$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimación de máxima verosimilitud (MLE)\n",
    "\n",
    "Asumase un modelo estadístico paramétrico $\\mathcal{P}=\\Big\\{f(x;\\theta): \\theta \\in \\Theta \\Big\\}$, el cual está asociado a las variables aleatorias $X_{1},..., X_{n}$. Asúmase que exista un parámetro $\\theta^{*} \\in \\Theta$ tal que $X \\sim P_{\\theta_{*}}$ es el verdadero parámetro. Nuestro objetivo es encontrar un estimador $\\hat{\\theta}=g(X_{1},...,X_{n})$ tal que $P_{\\hat{\\theta}} \\approx P_{\\theta^{*}}$:\n",
    "\n",
    "$$|P_{\\hat{\\theta}}(A) - P_{\\theta^{*}}(A)| \\approx 0$$\n",
    "\n",
    "Para todo $A$ en el dominio de las variables aleatorias $X$, denotado como E.\n",
    "\n",
    "Se define como la variacion de distancia total ($TV$) como:\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "$$ TV(P_{\\theta},P_{\\theta^{*}}) =   \\left\\{\n",
    "\\begin{array}{ll}\n",
    "      \\frac{1}{2}\\sum_{x\\in E}|P_{\\theta}(x) - P_{\\theta^{*}}(x)| & Si\\ x\\ es\\ discreto\\\\\n",
    "      \\frac{1}{2}\\int_{x\\in E}|f_{\\theta}(x) - f_{\\theta^{*}}(x)|dx & Si\\ x\\ es\\ continuo \\\\\n",
    "\\end{array} \n",
    "\\right.  $$\n",
    "\n",
    "\n",
    "El objetivo para encontrar un estimador de máxima verosimilitud es encontrar un estimador $\\hat{\\theta}$ que minimize la función $TV(P_{\\hat{\\theta}}, P_{\\theta^{*}})$.\n",
    "\n",
    "¿Cómo podemos calcular esta ecuación si no sabemos cuál es el parámetro real $\\theta^{*}$?\n",
    "\n",
    "\n",
    "**Divergencia de Kullback-Liebler**: La divergencia de Kullback-Liebler ($KL$) mide la divergencia entre dos distribuciones. En teoría de la información, mide cuánta información perdemos al utilizar una distribución en vez de la otra. \n",
    "\n",
    "\n",
    "$$ KL(P_{\\theta},P_{\\theta^{*}}) =   \\left\\{\n",
    "\\begin{array}{ll}\n",
    "      \\sum_{x\\in E}P_{\\theta^{*}}(x) \\log\\Big(\\frac{P_{\\theta^{*}}(x)}{P_{\\theta}}(x)\\Big) & Si\\ x\\ es\\ discreto\\\\\n",
    "      \\int_{x\\in E}f_{\\theta^{*}}(x)\\log\\Big(\\frac{f_{\\theta^{*}}(x)}{f_{\\theta}(x)}\\Big)dx & Si\\ x\\ es\\ continuo \\\\\n",
    "\\end{array} \n",
    "\\right.  $$\n",
    "\n",
    "Podemos observar que la divergencia de kullback liebler es una esperanza!\n",
    "\n",
    "$$KL(P_{\\theta},P_{\\theta^{*}}) = \\mathbb{E}\\Big[\\log\\Big(\\frac{P_{\\theta^{*}}(x)}{P_{\\theta}(x)}\\Big)\\Big] = \\mathbb{E}[\\log (P_{\\theta^{*}}(x))] - \\mathbb{E}[\\log (P_{\\theta}(x))]$$\n",
    "\n",
    "\n",
    "**OBS**: $\\mathbb{E}[\\log (P_{\\theta^{*}}(x))]$ es una constante (llamésmosla $c$)!\n",
    "\n",
    "Por ley de los grandes números: $\\mathbb{E}[\\log (P_{\\theta}(x))] \\rightarrow \\dfrac{1}{n}\\sum^{n}_{i=1}\\log (P_{\\hat{\\theta}}(x))$, mientras $n \\rightarrow \\infty$\n",
    "\n",
    "Así, podemos construir una divergencia aproximada que no depende del parámetro real $\\theta^{*}$:\n",
    "$$\\hat{KL}(P_{\\theta},P_{\\theta^{*}}) = c - \\dfrac{1}{n}\\sum^{n}_{i=1}\\log (P_{\\theta}(x))$$\n",
    "\n",
    "\n",
    "Podemos encontrar una aproximación a $\\theta^{*}$ minimizando la divergencia aproximada:\n",
    "\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "\\hat{\\theta} & = argmin_{\\theta}\\ - \\dfrac{1}{n}\\sum^{n}_{i=1}\\log (P_{\\theta}(x)) \\\\\n",
    " & = argmax_{\\theta}\\ \\dfrac{1}{n}\\sum^{n}_{i=1}\\log (P_{\\theta}(x)) \\\\\n",
    " & = argmax_{\\theta}\\ \\dfrac{1}{n}\\log \\Big(\\prod^{n}_{i=1}P_{\\theta}(x)\\Big) \\\\\n",
    " & = argmax_{\\theta}\\ \\prod^{n}_{i=1}P_{\\theta}(x)\n",
    "\\end{split} $$\n",
    "\n",
    "\n",
    "**$\\prod^{n}_{i=1}P_{\\theta}(x)$** es la verosimilitud!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Estadistica Bayesiana\n",
    "\n",
    "\n",
    "Hasta ahora, todo lo que hemos visto es estadística **frencuentista**: tenenos datos que son generados aleatoriamente y hacemos ciertas suposiciones acerca de ellos (alguna distribución, iid, etc). El proceso que genera estos datos está asociado a alguna distribución o los parámetros de esa distribucion. Con esto, podemos hacer inferencia sobre los datos.\n",
    "\n",
    "Desde el punto de vista **Bayesiano**: Tenemos un proceso generativo que tiene un parámetro y los datos son generados a partir de este parámetro. Se tiene un conocimiento **a priori** acerca del parámetro y este conocimiento a priori debiese cobrar menor importancia a medida que tenemos más datos. Usando los datos, queremos actualizar nuestro conocimiento a prior y convertirlo en un conocimiento **a posteriori**.\n",
    "\n",
    "\n",
    "La estadística bayesiana proviene (como su nombre lo dice) del teorema de bayes:\n",
    "$$P(\\theta|X_{1},...,X_{n}) = \\dfrac{P(X_{1},...,X_{n}|\\theta)P(\\theta)}{P(X_{1},...,X_{n})}$$\n",
    "\n",
    "\n",
    "donde:\n",
    "1. $P(\\theta|X_{1},...,X_{n})$: Posterior.\n",
    "2. $P(X_{1},...,X_{n}|\\theta)$: Likelihood.\n",
    "3. $P(\\theta)$: Prior.\n",
    "4. $P(X_{1},...,X_{n})$: Marginal.\n",
    "\n",
    "\n",
    "## Mamimo a posteriori (MAP)\n",
    "\n",
    "\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "\\hat{\\theta}^{MAP} & = argmax_{\\theta}\\ \\dfrac{P(X_{1},...,X_{n}|\\theta)P(\\theta)}{P(X_{1},...,X_{n})} \\\\\n",
    " & = argmin_{\\theta}\\ \\log{\\dfrac{P(X_{1},...,X_{n}|\\theta)P(\\theta)}{P(X_{1},...,X_{n})}} \\\\\n",
    " & \\propto argmin_{\\theta}\\ P(X_{1},...,X_{n}|\\theta)P(\\theta) \\\\\n",
    "\\end{split} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Distribución Beta')"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = 50, 50\n",
    "\n",
    "samples = np.random.beta(a=a, b=b, size=100000)\n",
    "\n",
    "plt.hist(samples, bins=100)\n",
    "plt.ylabel('Ocurrencias')\n",
    "plt.title('Distribución Beta')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}