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..



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?

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  • $\begingroup$ No, I don't think they're independent (I have to calculate Cov(X,Y)=E(XY)-E(X)E(Y) and it would be too simple if X and Y were independent :) ). $\endgroup$ – user111663 Nov 26 '13 at 18:41
  • $\begingroup$ In that case you haven't given us enough information to specify the distribution. $\endgroup$ – Robert Israel Nov 26 '13 at 18:48
  • $\begingroup$ +1 for answering a question about a simple problem with a hint rather than a full answer, even if it turned out only to force clarification by the OP. $\endgroup$ – Mars Jan 15 '14 at 18:12

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