### Simulate rolling a pair of fair dice.
# There are 12 possible outcomes. Let x be the sum of pips you see on each roll
# of the pair of fair dice.

n = 10000
x = matrix(sample(1:6,2*n,replace=T),2,n)
s = apply(x,2,sum)

br = (1:13)-0.5

par(mfcol=c(4,1))
hist(s[1:100],nclass=12,breaks=br,probability=T,main="relative frequency plot - roll a pair of dice")
hist(s[1:500],nclass=12,breaks=br,probability=T,main="relative frequency plot - roll a pair of dice")
hist(s[1:1000],nclass=12,breaks=br,probability=T,main="relative frequency plot - roll a pair of dice")
hist(s[1:10000],nclass=12,breaks=br,probability=T,main="relative frequency plot - roll a pair of dice")

p.obs = table(s)/n
p.exp = c(1,2,3,4,5,6,5,4,3,2,1)/36

cbind(p.obs,p.exp)