If $X$ and $Y$ are two (not necessarily independent) Bernoulli's with success probabilities $a$ and $b$ resp., how do we construct the joint dist. in terms of $a$,$b$, and $\rho$---the correlation?
I can get $\mathbb{P}(X=1,Y=1)$ by manipulating the expression for $\rho$, but lost for the other three...