6 Let Z and W be independent standard normal random variables. Let X and Y be defined by Y = 0 [pZ+ 1-p W] + H2 where , > 0, < 141 142 <00, and -1 < p < 1. Show that the joint probability density function of X and Y is bivariate normal and ox = 01, 0y=02, x = 1. My = 2, and p(X, Y) = p. Note: By this exercise, if the joint probability density function of X and Y is bivariate normal, X and Y can be written as sums of independent standard normal random variables.