Thread: Bivariate normal Distribution

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

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

Thanks in advance

Originally Posted by realfunboy

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

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

Thanks in advance

Several approaches are possible.

One approach might start by first proving that the two random variables and are independent and standard normal. Then note that if and only if .