Hello,

Look at the definition of correlation It's not because values are random that they're uncorrelated !! Imagine you choose the number X=2 randomly. It's multiplied by 2 in order to get a final result, Y. Thus the final result is chosen randomly at last ! Are X and Y uncorrelated ?

There is no relationship between uncorrelation and the distribution. Except if you have a certain case of random vector, but that's another story...