% PROGRAM TO DISPLAY THE POWER OF CENTRAL LIMIT THEOREM 

% Parameters and Storage Vectors
clc;
loops = 50000;
n = 1;
normmean = zeros(loops,1);
cc = 1;

% Loop to Draw from Chi-Square Probability Distribution
while cc <= loops
	x = (randn(n,1)).^2;
	meanx = mean(x);
	normmean(cc,1) = sqrt(n)*(meanx - 1)/sqrt(2);
	cc = cc + 1;
end

% Graph Sampling Distribution
hold on;
histogram(normmean,50,'Normalization','pdf');
title('Simulated Sampling Distribution of Transformed Mean from Chi-Square(1) pdf'); 

% Superimposing Standard Normal Probability Distribution 
xvalues = (-5:0.01:5); 
f = (1/sqrt(2*pi))*exp(-0.5*xvalues.^2);
plot(xvalues,f);