### Simulate rolling a fair die.
# There are six possible outcomes. Let x be the number of pips you see on each
# roll of a fair die.

n <- 10000
x <- sample(1:6,n,replace=T)

br <- (1:7)-0.5

par(mfcol=c(4,1))
hist(x[1:100],breaks=br,probability=T,main="relative frequency plot - roll one die")
hist(x[1:500],breaks=br,probability=T,main="relative frequency plot - roll one die")
hist(x[1:1000],breaks=br,probability=T,main="relative frequency plot - roll one die")
hist(x[1:10000],breaks=br,probability=T,main="relative frequency plot - roll one die")

p.obs <- table(x)/n
p.exp <- c(1,1,1,1,1,1)/6

cbind(p.obs,p.exp)