Let X and Y be independent standard normal random variables,and let
Z = aX + squarerootof(1-a^2)*Y
where 0 < a < 1.
Determine the region on the xy plane where X < Z?
Use this region to determine the E[max(X,Z)] that is to determine the maximum of X and Z.
I understand how to get the region and how to seperate the integrals, into the x and z integrals multiplying by the joint density function in each. The hint says that we should use polar co-ordinates but i have no idea how to get the limits of integration in this case? Any help would be much appreciated!