DAT 605 - Wk5, Discussion 5 - Trying to reply to James Mundy

CHAPTER 1. DISCRETE PROBABILITY DISTRIBUTIONS Page 12

• First let fix the convention:

0 = Tails and 1 = Heads

library(matlib)
library(MASS)
library(dplyr)
library(ggplot2)
library(patchwork)

Response to James Mundy

Observations:

• The first plot checks out in that as n increase, the proportion of heads minus 1/2 approaches zero

• Similar to James Mundy’s findings was that, as n increases, the # of heads minus the 1/2 the # of tosses increased

  counter-intuitively? As you can see in the simulation, as n gets bigger, so does the differences; not sure why?

set.seed(12345)



out1 <- c()
out2 <- c()
iter <- seq(100, 100000, 100)
for(n in iter) {
  num_heads <- rbinom(n, 1, 0.5)
  out1 <- c(out1, sum(num_heads)/n - 0.5)
  out2 <- c(out2, sum(num_heads) - (n/2))
}

df <- tibble(iter=iter, run1=out1, run2=out2)


p1 <- df %>% ggplot() + geom_line(aes(x=iter, y=run1), colour="blue") + theme_minimal()
p2 <- df %>% ggplot() + geom_line(aes(x=iter, y=run2), colour="red") + theme_minimal()
p1 / p2