9.16. Let X1 and X2 be independent random variables each having distribution Nu, 2). Let Z(t) = X cos wt + X2 sin cof. This random variable is of interest in the study of random signals. Let V(t) = dZ(t)/dt. (w is assumed to be constant.)

(a) What is the probability distribution of Z(t) and V(t) for any fixed r?

(b) Show that Z(t) and V(t) are uncorrelated. [Note: One can actually show that Z(t) and V(t) are independent but this is somewhat more difficult to do.]