Noori Selina

Discussion 8

  1. Write a program to toss a coin 10,000 times. Let Sn be the number of heads in the first n tosses. Have your program print out, after every 1000 tosses, Sn − n/2. On the basis of this simulation, is it correct to say that you can expect heads about half of the time when you toss a coin a large number of times?
n <- 1000
Sn <- c()
sum_heads <- 0
n_values <- c()

for (i in 1:10) {
  simulation <- sample(0:1, n, replace = TRUE)  # corrected 'replace' argument
  sum_heads <- sum_heads + sum(simulation == 1)
  Sn <- c(Sn, sum_heads / (n * i))
  n_values <- c(n_values, n * i)
}

data_frame <- data.frame(n_values, Sn)
data_frame
##    n_values        Sn
## 1      1000 0.5200000
## 2      2000 0.5185000
## 3      3000 0.5136667
## 4      4000 0.5132500
## 5      5000 0.5054000
## 6      6000 0.5060000
## 7      7000 0.5058571
## 8      8000 0.5103750
## 9      9000 0.5090000
## 10    10000 0.5102000