# Expectation of max(X, Y) where X and Y follow a joint normal distribution with correlation of $\rho$

As stated in the title, I am looking for the solution to this expectation, possibly as a function of $\rho$. One relevant solution I find is Lord Shark the Unknown's answer, from which I can derive $E(max(X, Y)) = \frac{1}{2}E(|V|)$. But I am not sure what to do next. Any suggestions?

• If $X$ and $Y$ have zero means and unit variances, then you might follow this answer:math.stackexchange.com/questions/382237/…. – StubbornAtom Aug 1 '18 at 19:09