#=====================================================
# R program to simulate the law of large numbers.
#=====================================================

#-----------------------------------------------------
# Simulate every number of trials from 5 to max.n.
# Store proportions of successes in p.obs.
#-----------------------------------------------------
p=.45          # Probability of success.
max.n=500      # Maximum number of trials.
n.vec=5:max.n  # Vector of numbers of trials.
p.obs=numeric(length(n.vec))
for (i in 1:length(n.vec)) {
  p.obs[i]=rbinom(1,n.vec[i],p)/n.vec[i]
}

#-----------------------------------------------------
# Plot p.obs versus n.vec.
#-----------------------------------------------------
plot(n.vec,p.obs,type="l",lty=1,xlab="number of trials",
  ylab="proportion of successes")
abline(h=p,lty=2)