Let Z N(0, 1) and (z) be its CDF. Let X N( = 3, ² = 9). (1a) It is known that (1.96) = 0.975. Find xsuch that P(X x) = 0.025. (1b) Let U = 3X + 1. Show that U has a normal distribution by deriving its MGF. (1c) Consider a transformed variable Y = e^1+2X. Find its expected value E(Y ).