Using Matlab prove that averaging the nth values of a uniform distribution approches a Gaussian distribution by averaging 2,4,6 and 8 nth values.

1. plot the resulting distribution profiles for each of the 4 cases on the same Matlab figure using the subplot command.

2. use 40 bins with the hist function

below is given matlab code;

N = 10000;

nu_bins = 40;

y = randn(1,N);

[ht,xout] = hist(y,nu_bins);

ht = ht/max(ht);

subplot(2,1,1);

bar(xout, ht);

ylabel('Occurance');

xlabel('x')

title('Gausian Distribution')

y = rand(1,N);

[ht,xout] = hist(y,nu_bins);

ht = ht/max(ht);

subplot(2,1,2);

bar(xout, ht);

ylabel('Occurance');

xlabel ('x');