Prove central limit theorem

How do I make an attempt to prove the central limit theorm for following uniform variables? Their dimension are different and the size of the matrix, not necessarily has to be same.

IonTimeLaserD=randi(1,100)%miliseconds
IonTimeIonization=randi(1,100) %miliseconds
KEinitialKEinitial=randi(1,50) %0eV
Flightspeed=randi(1,50) %cm/s

[Star Strider]

Use the conv (link) function to convolve them, and histogram (link) to see the result of the convolutions.

[Chanaka Navarathna]

I am not following much. To use conv function I have to use vectors on the brackets right? Can you show me an example? Thank you

[Star Strider]

Try this:

v = rand(1, 10)-0.5;
c{1} = v;
for k = 2:50
    c{k} = conv(c{k-1},v);
end

figure
histogram(c{end}, 21)

[John D'Errico]

Note that you won't theoretically "prove" the CLT by simple random sampling. A proof would require the use of limits.

[Star Strider]

‘prove’ = ‘illustrate’

[John D'Errico]

Um, no. I must disagree. :)

If the two were equivalent, then a picture of a pile of gold would be as good as that pile of gold. A picture of piles of currency in my private bank vault might serve to convince you that I MIGHT be rich, but it would not be proof of fact.

An illustrative example is nice, and it may convince you there is some meat behind an idea. But it is not a proof.