Example 1: Sum of two uniform random variables: X=U1+U2.
res.sum2=sum(rand(2,100000)); hist(res.sum2); hist(res.sum2,100);
Here is what the output looked like for one of my simulations:
Notice the form of the histogram. It is very close to a triangle.
%And for 10 uniforms: res.sum10=sum(rand(10,100000)); hist(res.sum10); hist(res.sum10,100); %Is for commentsHere is what the output looked like for one of my simulations: