Not really a homework question, but here goes... 1. The problem statement, all variables and given/known data If we have two (binary) random variables X and Y, and we know the probability mass function for X, as well as the correlation between X and Y, can we find the probability mass function for Y? 2. Relevant equations Let f(x) be the mass function for X and g(y) be the mass function for Y. Let g(1) = q and g(0) = 1-q. Given f(1) = p and f(0) = 1-p, and that the correlation between X and Y is c, can we find q as a function of p and c (only)? 3. The attempt at a solution Let h(x,y) be the joint distribution of X and Y. We can show that that Cov(X,Y) = h(1,1)-pq, and so Corr(X,Y) = [h(1,1)-pq]/sqrt[pq(1-p)(1-q)] = c. Where to go from there? Seems as if we have one equation with two unknowns. (Is there another equation lurking somewhere?) Thanks for any help folks.