1. (20 pts) Suppose {Zt, t = Z} are i.i.d standard normal random variables N(0, 1). Consider a process {Xt, t = Z}, such that Xt = ZtZt-1 + Zt cos wt + Zt-1 sin wt, where w is a deterministic constant. (a) (10 pts) Find the acvf of Xt. Hint: sin(a) cos(b) = 1/2[sin(a + b) + sin(a b)]. (b) (5 pts) Is Xt stationary? Discuss the problem for different values of w. (c) (5 pts) Set w = / - /2. Find the best linear predictor of Xt in terms of (Xt-1, Xt-2).