Let x and y have a bivariate normal distribution and suppose that x and y both have mean 0 and variance 1, so that their marginal distributions arc standard normal and their joint density is 

Show that if the correlation coefficient between x and y is p, then that between x² and y² is p².

p(x, y) = {2 (1-p)}" exp{-1 (x 2pxy + y)/(1 p)}. .