How to use uniform distribution to see central limit theorem in action?

Question

I would like to use MATLAB to visualize the Central Limit Theorem in action. I would like to use rand() to produce 10 samples of uniform distribution U[0,1] and compute their average, then save it to a matrix 'Mat'.

I would then use a histogram to visualize the convergence in distribution. How would you do this and normalize that histogram so it is a valid probability density (instead of just counting the frequency of occurrence)?

To generate the samples I am doing something like:

Mat = rand(N,sizeOfVector) > rand(1);

But I guess I am going to the wrong side.

Answer 1

To generate N samples of length sizeOfVector you start out with rand as you suggested, and then continue as follows (calling the array average instead of Mat for readability):

samples = rand(N,sizeOfVector);

average = mean(samples,1);

binWidth = 3.49*std(average)*N^(-1/3)); %# Scott's rule for good bin width for normal data
nBins = ceil((max(average)-min(average))/binWidth);

[counts,x] = hist(average,nBins);

normalizedCounts = counts/sum(counts);

bar(x,normalizedCounts,1)