(b) Let / E R and o > 0. Let U and V be independent random variables each having N(u, 02) distribution with the moment generating functions My(t) and My(t), respectively given by Mu(t) = My(t) = etutino, toR. (i) Compute the distribution of U - 2V. Justify your answer. (ii) Let Z ~ N(0, 1) and let Mz(t) be the the moment generating function of Z. Show that MS) (t) = tM,2) (t) + 2M2 (t), ter, M2" (t) = tM2 (t) + 3M2 (t), ter, and state E(Z* ), k = 1, 2, 3, 4. (iii) Compute corr(1 + Z + Z2, 1 - Z + Z2)