Coin Toss

An introduction

What is the limiting distribution of getting heads in a coin toss? You can either land on heads or tails. Our sample space here is \(S = \{H, T\}\), and we define this in R:

S <- c("H", "T")

We want to randomly select a head or tail: (note: I am using set.seed to get reproducible results)

set.seed(1)
sample(S, size = 1)

[1] "H"

We flip our coin and we land on a head! After one toss, the relative frequency of landing on a head is \(\frac{1}{1} = 1\). Let’s flip our coin again:

sample(S, size = 1)

[1] "T"

We get a tail this time. Therefore, after two tosses, the relative frequency of landing on a head is \(\frac{1}{2} = 0.5\). Let’s do one more coin toss..

sample(S, size = 1)

[1] "H"

Our coin lands on a head. Therefore, after three tosses, the relative frequency of landing on a head is \(\frac{2}{3} = 0.67\).

Using a `for` loop to achieve multiple (1000) coin tosses

library(tidyverse)

head_vals <- c()
head_prob <- c()
for (i in 1:1000){
head_vals <- c(head_vals, sample(S, 1))

## number of times a head appears in head_vals:
n_heads <- str_count(head_vals, pattern = "H") %>% sum()

head_prob <- c(head_prob, n_heads/i)
}

tibble(sim = 1:1000, head_prob) %>%
  ggplot(aes(x = sim, y = head_prob)) + 
  geom_line() + 
  geom_hline(yintercept = 0.5, colour = "red")

An introduction

Using a for loop to achieve multiple (1000) coin tosses

Using a `for` loop to achieve multiple (1000) coin tosses