# Product of 2 Binomial distributions

I was wondering what the distribution is of the product of two binomial distributed random variables, X and Y; So suppose X ~ Bin(n,p1) and Y ~ Bin(n,p2) (so the number of experiments n is the same), what can we say about the distribution of XY?

I have to calculate E(XY) and I don't see another method then finding the distribution of XY, which seems quite difficult to me..

Thanks.

Hint: are $X$ and $Y$ supposed to be independent? What do you know about the expected value of the product of two independent random variables?