Simulation of Probability Estimate with Repeated Experiments (Coin Toss)

binomial_frequentist_simulation.R

library(tidyverse)

set.seed(100)
df <- tibble(
  n = seq(1e5),
  x = rbinom(1e5, 1, 0.5), 
  y = cumsum(x) / n
)

## In base R, plot(df$n, df$y)
ggplot(df, aes(x = n, y = y)) + 
  geom_point() + 
  xlab("Number of Trials") + 
  ylab("Estimated Probability of Heads") + 
  scale_y_continuous(
    limits = c(0, 0.6),
    breaks = seq(0, 0.6, by = 0.1)
  )