### Simulate flipping a fair coin.
# There are two possible outcomes. Let x be the number of heads in n flips of a
# fair coin.

n <- 500
x <- sample(0:1,n,replace=T)
p.hat <- cumsum(x)
index <- 1:n
p.hat <- p.hat/index

plot(p.hat,main="relative frequency of heads",type="l",ylim=c(0,1))

p.obs <- p.hat[n]
p.exp <- 1/2

cbind(p.obs,p.exp)