#4. Sample Variance and degrees of freedom
#Histogram of s^2 for normal population of size n
#Histogram of \hat \sigma^2 (with n in denominator) for normal populaion of size n.
#
par(mfrow=c(1,1))
n=3
nsamp=1000
ssquared=NULL
for(iter in 1:nsamp)
  ssquared=c(ssquared,var(rnorm(n)))
hist(ssquared, main = paste("1000 Replications of Sample Variance, n=3
Vertical lines at 1, Mean of Sample Variance =",(round(mean(ssquared),3))),
xlab="Sample Variance")
abline(v=mean(ssquared))
abline(v=1)
title(sub="Population is Standard Normal")
#