# Math Help - Bivariate normal Distribution

1. ## Bivariate normal Distribution

Show that for standard bivariate normal variables X and Y with correlation "rho"

E(max(X,Y)) = sqrt((1-rho)/pi)

One approach might start by first proving that the two random variables $X$ and $U = \frac{Y - \rho X}{\sqrt{1 - \rho^2}}$ are independent and standard normal. Then note that $Y > X$ if and only if $(1 - \rho) X < \sqrt{1 - \rho^2} U$.