run all code through styler for consistency

03_limits.qmd

@@ -57,12 +57,14 @@ means <- cumsum(Xs) / 1:n
 
 ggplot(tibble(n = 1:n, estimate = means), aes(x = n, y = estimate)) +
   geom_line() +
-  scale_x_continuous(labels = comma, limit = c(0, n*1.1), breaks = seq(0, n, length.out = 5)) +
+  scale_x_continuous(labels = comma, limit = c(0, n * 1.1), breaks = seq(0, n, length.out = 5)) +
   scale_y_continuous(limits = c(0, 1)) +
-  annotate(geom = "text", x = 1.1*n, y = means[n], label = glue("Estimate at\nn = {comma(n)}", ":\n", means[n]), size = 2.8) +
+  annotate(geom = "text", x = 1.1 * n, y = means[n], label = glue("Estimate at\nn = {comma(n)}", ":\n", means[n]), size = 2.8) +
   annotate(geom = "point", x = n, y = means[n]) +
-  labs(x = "n, or the number of times of a coin-flip experiment", 
-       y =  "Estimate of the Probability of Heads after n trials")
+  labs(
+    x = "n, or the number of times of a coin-flip experiment",
+    y = "Estimate of the Probability of Heads after n trials"
+  )
 ```
 
 ## Sequences
@@ -90,16 +92,16 @@ We find the sequence by simply "plugging in" the integers into each $n$. The imp
 #| echo: false
 #| fig-cap: Behavior of Some Sequences
 seq <- 1:20
-df <- tibble(n = seq, A = 2 - 1/(seq^2), B = (seq^2 + 1)/(seq), C = (-1)^seq * (1 - 1/seq))
+df <- tibble(n = seq, A = 2 - 1 / (seq^2), B = (seq^2 + 1) / (seq), C = (-1)^seq * (1 - 1 / seq))
 
-g0 <- ggplot(df, aes(x = n, y = A)) + geom_point()
+g0 <- ggplot(df, aes(x = n, y = A)) +
+  geom_point()
 
 gA <- g0 + labs(y = expression(A[n]))
 gB <- g0 + aes(y = B) + labs(y = expression(B[n]))
 gC <- g0 + aes(y = C) + labs(y = expression(C[n]))
 
 gA + gB + gC + plot_layout(nrow = 1)
-
 ```
 
 ## The Limit of a Sequence
@@ -230,13 +232,13 @@ range2 <- tibble::tibble(x = c(-2, 2))
 
 fx1 <- ggplot(range1, aes(x = x)) +
   stat_function(fun = function(x) sqrt(x), size = 0.5) +
-  labs(x = expression(x), y = expression(f(x)), title = expression(f(x)==sqrt(x))) +
+  labs(x = expression(x), y = expression(f(x)), title = expression(f(x) == sqrt(x))) +
   expand_limits(y = max(range1$x))
 
-fx2 <- 
+fx2 <-
   ggplot(range2, aes(x = x)) +
-  stat_function(fun = function(x) ifelse(x == 0, NA, 1/x), size = 0.5) +
-  labs(x = expression(x), y = expression(f(x)), title = expression(f(x)==frac(1,x)))
+  stat_function(fun = function(x) ifelse(x == 0, NA, 1 / x), size = 0.5) +
+  labs(x = expression(x), y = expression(f(x)), title = expression(f(x) == frac(1, x)))
 
 fx1 + fx2 + plot_layout(nrow = 1)
 ```
@@ -282,21 +284,21 @@ range4 <- tibble(x = c(0, 5))
 
 fx1 <- ggplot(range1, aes(x = x)) +
   stat_function(fun = function(x) sqrt(x), size = 0.5) +
-  labs(y = expression(f(x)), title = expression(f(x)==sqrt(x)))
+  labs(y = expression(f(x)), title = expression(f(x) == sqrt(x)))
 
 fx2 <- ggplot(range2, aes(x = x)) +
   stat_function(fun = function(x) exp(x), size = 0.5) +
-  labs(y = expression(f(x)), title = expression(f(x)==e^x))
+  labs(y = expression(f(x)), title = expression(f(x) == e^x))
 
 fx3 <- ggplot(range3, aes(x = x)) +
-  stat_function(fun = function(x) ifelse(x == 0, NA, 1 + 1/(x^2)), size = 0.5) +
-  labs(y = expression(f(x)), title = expression(f(x)==1+frac(1,x^2)))
+  stat_function(fun = function(x) ifelse(x == 0, NA, 1 + 1 / (x^2)), size = 0.5) +
+  labs(y = expression(f(x)), title = expression(f(x) == 1 + frac(1, x^2)))
 
 fx4 <- ggplot(range4, aes(x = x)) +
   stat_function(fun = function(x) ifelse(1 - (x %% 1) < 9e-2, NA, floor(x)), size = 0.5) +
   geom_point(data = tibble(x = 0:5, y = 0:5), aes(y = y), pch = 19) +
   geom_point(data = tibble(x = 1:5, y = (1:5) - 1), aes(y = y), pch = 21, fill = "white") +
-  labs(y = expression(f(x)), title = expression(f(x)==plain("floor(x)")))
+  labs(y = expression(f(x)), title = expression(f(x) == plain("floor(x)")))
 
 fx1 + fx2 + fx3 + fx4 + plot_layout(ncol = 2)
 ```
@@ -329,7 +331,6 @@ Example @exm-seqbehav
 Exercise @exr-limseq2
 
 ```{r}
-
 ```
 
 Example @exm-limfun1
@@ -370,7 +371,7 @@ Divide each part by $x$, and we get $x + \frac{2}{x}$ on the numerator, $1$ on t
 range0 <- tibble(x = c(-4, 2))
 
 ggplot(range0, aes(x = x)) +
-  stat_function(fun = function(x) ifelse(x == 0, NA, (x^2 + 2*x)/(x)), size = 0.5) +
-  labs(y = expression(f(x)), title = expression(f(x)==frac(x^2+2*x, x^2))) +
-    geom_point(data = tibble(x = 0, y = 2), aes(y = y), pch = 21, fill = "white")
+  stat_function(fun = function(x) ifelse(x == 0, NA, (x^2 + 2 * x) / (x)), size = 0.5) +
+  labs(y = expression(f(x)), title = expression(f(x) == frac(x^2 + 2 * x, x^2))) +
+  geom_point(data = tibble(x = 0, y = 2), aes(y = y), pch = 21, fill = "white")
 ```

04_calculus.qmd

@@ -56,21 +56,21 @@ range <- tibble::tibble(x = c(-3, 3))
 fx0 <- ggplot(range, aes(x = x)) +
   labs(x = expression(x), y = expression(f(x)))
 
-fx <- fx0 +  
-  stat_function(fun = function(x) 2*x, size = 0.5) +
+fx <- fx0 +
+  stat_function(fun = function(x) 2 * x, size = 0.5) +
   labs(title = "f(x) = 2x") +
   expand_limits(y = 0)
 
 fprimex <- fx0 + stat_function(fun = function(x) 2, size = 0.5, linetype = "dashed") +
-  labs(x = expression(x), y = expression(f~plain("'")~(x)))
+  labs(x = expression(x), y = expression(f ~ plain("'") ~ (x)))
 
-gx <- fx0 +  
+gx <- fx0 +
   stat_function(fun = function(x) x^3, size = 0.5) +
-  labs(y = expression(g(x)), title = expression(g(x)==x^3)) +
+  labs(y = expression(g(x)), title = expression(g(x) == x^3)) +
   expand_limits(y = 0)
 
-gprimex <- fx0 + stat_function(fun = function(x) 3*(x^2), size = 0.5, linetype = "dashed") +
-  labs(x = expression(x), y = expression(g~plain("'")~(x)))
+gprimex <- fx0 + stat_function(fun = function(x) 3 * (x^2), size = 0.5, linetype = "dashed") +
+  labs(x = expression(x), y = expression(g ~ plain("'") ~ (x)))
 
 fx + fprimex + gx + gprimex + plot_layout(ncol = 2)
 ```
@@ -246,15 +246,17 @@ To repeat the main rule in Theorem @thm-derivexplog, the intuition is that
 range <- tibble::tibble(x = c(-3, 3))
 
 fx0 <- ggplot(range, aes(x = x)) +
-  labs(x = expression(x), y = expression(f(x)),
-       caption = expression(f(x)==e^x))
+  labs(
+    x = expression(x), y = expression(f(x)),
+    caption = expression(f(x) == e^x)
+  )
 
-fx <- fx0 +  
+fx <- fx0 +
   stat_function(fun = function(x) exp(x), size = 0.5) +
   expand_limits(y = 0)
 
 fprimex <- fx0 + stat_function(fun = function(x) exp(x), size = 0.5) +
-  labs(x = expression(x), y = expression(f~plain("'")~(x)))
+  labs(x = expression(x), y = expression(f ~ plain("'") ~ (x)))
 
 fx + fprimex + plot_layout(nrow = 1)
 ```
@@ -286,15 +288,17 @@ The natural log is the mirror image of the natural exponent and has mirroring pr
 range <- tibble::tibble(x = c(-0.1, 3))
 
 fx0 <- ggplot(range, aes(x = x)) +
-  labs(x = expression(x), y = expression(f(x)),
-       caption = expression(f(x)==log(x)))
+  labs(
+    x = expression(x), y = expression(f(x)),
+    caption = expression(f(x) == log(x))
+  )
 
-fx <- fx0 +  
+fx <- fx0 +
   stat_function(fun = function(x) ifelse(x <= 0, NA, log(x)), size = 0.5) +
   expand_limits(y = 0)
 
-fprimex <- fx0 + stat_function(fun = function(x) ifelse(x <= 0, NA, 1/x), size = 0.5) +
-  labs(x = expression(x), y = expression(f~plain("'")~(x)))
+fprimex <- fx0 + stat_function(fun = function(x) ifelse(x <= 0, NA, 1 / x), size = 0.5) +
+  labs(x = expression(x), y = expression(f ~ plain("'") ~ (x)))
 
 fx + fprimex + plot_layout(nrow = 1)
 ```
@@ -473,10 +477,10 @@ fx <- ggplot(range1, aes(x = x)) +
   labs(y = expression(f(x)))
 
 Fx <- ggplot(range1, aes(x = x)) +
-  stat_function(fun = function(x) (x^3)/3 - 4*x,     size = 0.5, linetype = "dashed") +
-  stat_function(fun = function(x) (x^3)/3 - 4*x + 1, size = 0.5, linetype = "dotted") +
-  stat_function(fun = function(x) (x^3)/3 - 4*x - 1, size = 0.5, linetype = "dotdash") +
-  labs(y = expression(integral(f(x)*dx)))
+  stat_function(fun = function(x) (x^3) / 3 - 4 * x, size = 0.5, linetype = "dashed") +
+  stat_function(fun = function(x) (x^3) / 3 - 4 * x + 1, size = 0.5, linetype = "dotted") +
+  stat_function(fun = function(x) (x^3) / 3 - 4 * x - 1, size = 0.5, linetype = "dotdash") +
+  labs(y = expression(integral(f(x) * dx)))
 
 fx + Fx + plot_layout(ncol = 1)
 ```
@@ -516,23 +520,23 @@ Suppose we want to determine the area $A(R)$ of a region $R$ defined by a curve
 #| label: fig-defintfig
 #| echo: false
 #| fig-cap: The Riemann Integral as a Sum of Evaluations
-f3 <- function(x) -15*(x - 5) + (x - 5)^3 + 50
+f3 <- function(x) -15 * (x - 5) + (x - 5)^3 + 50
 
-d1 <- tibble(x = seq(0, 10, 1)) %>%  mutate(f = f3(x))
-d2 <- tibble(x = seq(0, 10, 0.1)) %>%  mutate(f = f3(x))
+d1 <- tibble(x = seq(0, 10, 1)) %>% mutate(f = f3(x))
+d2 <- tibble(x = seq(0, 10, 0.1)) %>% mutate(f = f3(x))
 
 range <- tibble::tibble(x = c(0, 10))
 
 fx0 <- ggplot(range, aes(x = x)) +
   labs(x = expression(x), y = expression(f(x)))
 
-fx <- fx0 +  
-  expand_limits(y = 0) + 
+fx <- fx0 +
+  expand_limits(y = 0) +
   scale_y_continuous(expand = c(0, 0)) +
   scale_x_continuous(expand = c(0, 0))
 
-g1 <- fx +   geom_col(data = d1, aes(x, f), width = 1, fill = "gray", alpha = 0.5, color = "black") +   stat_function(fun = f3, size = 1.5) + labs(title = "Evaluating f with width = 1 intervals")
-g2 <- fx +   geom_col(data = d2, aes(x, f), width = 0.1, fill = "gray", alpha = 0.5, color = "black")  +   stat_function(fun = f3, size = 1.5) +labs(title = "Evaluating f with width = 0.1 intervals")
+g1 <- fx + geom_col(data = d1, aes(x, f), width = 1, fill = "gray", alpha = 0.5, color = "black") + stat_function(fun = f3, size = 1.5) + labs(title = "Evaluating f with width = 1 intervals")
+g2 <- fx + geom_col(data = d2, aes(x, f), width = 0.1, fill = "gray", alpha = 0.5, color = "black") + stat_function(fun = f3, size = 1.5) + labs(title = "Evaluating f with width = 0.1 intervals")
 
 g1 + g2 + plot_layout(nrow = 1)
 ```

05_optimization.qmd

@@ -91,14 +91,16 @@ So for example, $f(x) = x^2 + 2$ and $f^\prime(x) = 2x$
 #| fig-cap: Maxima and Minima
 range <- tibble::tibble(x = c(-3, 3))
 fx0 <- ggplot(range, aes(x = x)) +
-  labs(x = expression(x), y = expression(f(x)),
-       labs = expression(f(x)==x^2+2)) 
-fx <- fx0 +  
+  labs(
+    x = expression(x), y = expression(f(x)),
+    labs = expression(f(x) == x^2 + 2)
+  )
+fx <- fx0 +
   stat_function(fun = function(x) x^2 + 2, linewidth = 0.5) +
   expand_limits(y = 0)
 
-fprimex <- fx0 + stat_function(fun = function(x) 2*x, linewidth = 0.5, linetype = "dashed") +
-  labs(x = expression(x), y = expression(f~plain("'")~(x)))
+fprimex <- fx0 + stat_function(fun = function(x) 2 * x, linewidth = 0.5, linetype = "dashed") +
+  labs(x = expression(x), y = expression(f ~ plain("'") ~ (x)))
 
 fx + fprimex + plot_layout(nrow = 1)
 ```
@@ -117,14 +119,14 @@ fx0 <- ggplot(range, aes(x = x)) +
   labs(x = expression(x), y = expression(f(x))) +
   theme_bw()
 
-fx <- fx0 +  
+fx <- fx0 +
   stat_function(fun = function(x) x^3 + x^2 + 2, size = 0.5) +
   expand_limits(y = 0)
 
-fprimex <- fx0 + stat_function(fun = function(x) 3*x^2, size = 0.5, linetype = "dashed") +
-  labs(x = expression(x), y = expression(f~plain("'")~(x)))
+fprimex <- fx0 + stat_function(fun = function(x) 3 * x^2, size = 0.5, linetype = "dashed") +
+  labs(x = expression(x), y = expression(f ~ plain("'") ~ (x)))
 
-fx + fprimex + plot_annotation(expression(f(x)==x^3+2))
+fx + fprimex + plot_annotation(expression(f(x) == x^3 + 2))
 ```
 
 The second derivative $f''(x)$ identifies whether the function $f(x)$ at the point $x$ is
@@ -179,7 +181,7 @@ A function $f$ is strictly concave over the set S \underline{if} $\forall x_1,x_
 range1 <- tibble(x = c(-4, 4))
 fx1 <- ggplot(range1, aes(x = x)) +
   stat_function(fun = function(x) -x^2, size = 0.5) +
-  labs(y = expression(f(x)), title  = "Concave")
+  labs(y = expression(f(x)), title = "Concave")
 fx2 <- ggplot(range1, aes(x = x)) +
   stat_function(fun = function(x) x^2, size = 0.5) +
   labs(y = expression(f(x)), title = "Convex")

06_probability.qmd

@@ -126,7 +126,7 @@ Consider subsets A {2, 8} and B {2,3,7} of the sample space you found. What is
 #| echo: false
 #| fig-cap: Probablity as a Measure^[Images of Probability and Random Variables drawn
 #|   by Shiro Kuriwaki and inspired by Blitzstein and Morris]
-knitr::include_graphics('images/probability.png')
+knitr::include_graphics("images/probability.png")
 ```
 
 ### Probability Definitions: Formal and Informal {.unnumbered}
@@ -324,7 +324,7 @@ Most questions in the social sciences involve events, rather than numbers per se
 #| label: fig-rv-image
 #| echo: false
 #| fig-cap: The Random Variable as a Real-Valued Function
-knitr::include_graphics('images/rv.png')
+knitr::include_graphics("images/rv.png")
 ```
 
 ::: {#def-rv}
@@ -757,14 +757,13 @@ range <- tibble::tibble(x = c(-5, 5))
 fx0 <- ggplot(range, aes(x = x)) +
   labs(x = expression(x), y = expression(f(x)))
 
-fx <- fx0 +  
+fx <- fx0 +
   stat_function(fun = function(x) dnorm(x, mean = 0, sd = 1), linewidth = 0.5) +
   stat_function(fun = function(x) dnorm(x, mean = 0, sd = sqrt(2)), linewidth = 1.5) +
   expand_limits(y = 0) +
   labs(caption = "Thick line: variance = 2, Normal line: variance = 1")
 
 fx
-
 ```
 
 ## Summarizing Observed Events (Data)

11_data-handling_counting.qmd

@@ -102,7 +102,7 @@ R is an object oriented programming language primarily used for statistical comp
 -   Different objects have different allowable procedures:
 
 ```{r}
-# Adding a string and a string does not work because the '+' operator 
+# Adding a string and a string does not work because the '+' operator
 # does not work for strings:
 
 # 'Harvard' + 'Gov'
@@ -114,7 +114,7 @@ R is an object oriented programming language primarily used for statistical comp
 x <- 9
 class(9)
 class(x)
-class('Harvard')
+class("Harvard")
 ```
 
 Object oriented programming makes languages flexible and powerful:
@@ -143,7 +143,6 @@ n_pb <- 3
 n_jelly <- 9
 
 # write instructions in R here
-
 ```
 
 ## Base-R vs. tidyverse
@@ -271,7 +270,8 @@ dim(ober)
 From your tutorials, you also know how to do graphics! Graphics are useful for grasping your data, but we will cover them more deeply in Chapter @sec-dataviz.
 
 ```{r}
-ggplot(ober, aes(x = Fame)) + geom_histogram()
+ggplot(ober, aes(x = Fame)) +
+  geom_histogram()
 ```
 
 What about the distribution of fame by regime?
@@ -312,10 +312,12 @@ First get a map of the Greek world.
 #| message: false
 #| warning: false
 #| eval: false
-greece <- get_map(location = c(lon = 22.6382849, lat = 39.543287),
-                  zoom = 5, 
-                  source = "stamen",
-                  maptype = "toner")
+greece <- get_map(
+  location = c(lon = 22.6382849, lat = 39.543287),
+  zoom = 5,
+  source = "stamen",
+  maptype = "toner"
+)
 ggmap(greece)
 ```
 
@@ -329,12 +331,14 @@ Ober's data has the latitude and longitude of each polis. Because the map of Gre
 #| warning: false
 #| eval: false
 gg_ober <- ggmap(greece) +
-  geom_point(data = ober, 
-             aes(y = Latitude, x = Longitude), 
-             size = 0.5,
-             color = "orange")
-gg_ober + 
-  scale_x_continuous(limits = c(10, 35)) + 
+  geom_point(
+    data = ober,
+    aes(y = Latitude, x = Longitude),
+    size = 0.5,
+    color = "orange"
+  )
+gg_ober +
+  scale_x_continuous(limits = c(10, 35)) +
   scale_y_continuous(limits = c(32, 44)) +
   theme_void()
 ```