#5. Central Limit Theorem
#
#Histogram of averages of size 5, 25 from N(0,1) population
#Histogram of averages of size 5, 25 from t(2) population
#                                         t(1) population
#
par(mfrow=c(3,1))
nsamp=10000
n=5
xbar5=NULL
for(iter in 1:nsamp)
  xbar5=c(xbar5,mean(rnorm(n)))
n=25
xbar25=NULL
for(iter in 1:nsamp)
  xbar25=c(xbar25,mean(rnorm(n)))
plot(seq(-2,2,.001),dnorm(seq(-2,2,.001)),type="l",main="Standard Normal Population",cex.main=1.8,ylab="Density")
abline(v=0)
hist(xbar5,xlim=c(-2,2),main="Sample Mean, n=5",cex.main=1.8)
abline(v=0)
mtext("Mean=",at=c(-1,1000))
mtext(round(mean(xbar5),3),at=c(-.7,1000))
mtext("SD=",at=c(.7,1000))
mtext(round(sqrt(var(xbar5)),3),at=c(1,1000))
hist(xbar25,xlim=c(-2,2),main="Sample Mean, n=25",cex.main=1.8)
abline(v=0)
mtext("Mean=",at=c(-1,1000))
mtext(round(mean(xbar25),3),at=c(-.7,1000))
mtext("SD=",at=c(.7,1000))
mtext(round(sqrt(var(xbar25)),3),at=c(1,1000))
#