% SAMPLING DISTRIBUTION FOR AN ESTIMATOR OF SIGMA^2 

clc;
n = 5;
loops = 5000;
z = zeros(loops,2);
 
for ii = (1:1:loops)
  x = randn(n,1);
  s2 = (1/(n-1))*sum((x-mean(x)).^2);
  sigmahat2 = (1/n)*sum((x-mean(x)).^2);
  z(ii,1) = s2;
  z(ii,2) = sigmahat2;
end

subplot(2,1,1);
hist(z(:,1),30);
xlim([0,4]);
set(gca,'XTick',(0:1:4));
title(['Sampling distribution for s^2 when n = ',num2str(n)]);

subplot(2,1,2);
hist(z(:,2),30);
xlim([0,4]);
set(gca,'XTick',(0:1:4));
title(['Sampling Distribution for sigmahat^2 when n = ',num2str(n)]);