1. The problem statement, all variables and given/known data This is actually not a homework problem, but as it is very basic material, I post it here. I have two variables each with its marginal probability (estimated from data). I also have the correlation (variable). 2. Relevant equations How to find the joint/conditional probability? 3. The attempt at a solution I know either one of the joint or the conditional suffices due to Bayes' rule. Basically, my problem is that correlation would give me E(XY) since I know their variances from the marginal distribution. However, there are infinitely many joint distributions that could lead to this E(XY) and I don't know how to find the one consistent with the marginals.