Hello, I am trying to find an upper bound on the expectation value of the product of two random variables.

So suppose x, y are two non-independent random variables, given that I know the distribution of x p(x) and the distribution of y q(y), how can I find an upper bound on E[|x * y |] that is a function of p and q?

What inequality shall I use?

Thank you! Best Michele

Hello, I am trying to find an upper bound on the expectation value of the product of two random variables.

So suppose x, y are two non-independent random variables, given that I know the distribution of x p(x) and the distribution of y q(y), how can I find an upper bound on E[|x * y |] that is a function of p and q?

I know that Holder's inequality gives an upper bound to my problem in terms of moments of x and y, but this is a poor bound for the problem that I am considering.

Thank you! Best Michele