Problem number 5

and tan 1 (Y/X). 5. Let U, Z be independent random variables such that U is uniform on (0, 27) and Z is exponential with mean 1. Show that X = v2Z cos U and Y = v2Z sin U are independent standard normal random variables. T.et Y be independent random variables, both uniform on (0, 1). Compute the joint density of YILY