3. Let Zt be iid normal random variables and define: Zt, if t is even; Xt = (ZZ_1-1) V2 if t is odd. (a) (3 pts) Find E(Xt) and Var(Xt). When you compute Var(Xt), use the fact that E(ZA) = 3. (b) (3 pts) Show that Xt's are uncorrelated, that is, Cov(Xt, X,) = 0 for all t # s. doesn't depersson I so this process is (c) (3 pts) Show that Xt's are not independent. To prove this claim, you have to show that for any t * s ft,s(t, s) = ft(xt) f.(s) where fts is a joint density function of Xt, Xs while ft and fs are marginal density functions of Xt and Xs, respectively. However, there is an alternative (actually, much easier) way to prove this claim. Check whether Xt is a function of some other Xs, s / t. For example, check whether X5 is a function of other Xs, that is, X1, X2, X3, or X4. (d) (1 pt) Wrapping up (a)-(c) all together, conclude that {Xt} is WN(0,1) but not IID(0, 1)