### 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],nclass=6,breaks=br,probability=T,main="relative frequency plot - roll one die")
hist(x[1:500],nclass=6,breaks=br,probability=T,main="relative frequency plot - roll one die")
hist(x[1:1000],nclass=6,breaks=br,probability=T,main="relative frequency plot - roll one die")
hist(x[1:10000],nclass=6,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)