4
$\begingroup$

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.

$\endgroup$
3
$\begingroup$

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?

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.