####################
#   R CODE TO ILLUSTRATE THE BAYESIAN CENTRAL LIMIT THEOREM
#    USING BETA/BINOMIAL (HAMBURGER PATTIES) EXAMPLE
####################

x <- seq(0,1,length=100);
plot(x,dbeta(x,14,4),type="l",lty=1,xlab=expression(theta),
  ylab="posterior density")
phat <- 13/16;  var <- phat*(1-phat)/16
lines(x,dnorm(x,phat,sqrt(var)),lty=2)
legend(0 ,3.5,cex=1.2,legend =c(
 "exact (beta)", "approximate (normal)"),lty=1:2)