b. (7 points) Consider a random variable Y with probability density function (PDF): _ eye\"5 if y > 0, fv!) _ { 0 otherwise. (i) Determine the value of c. (ii) Completely specify the cumulative distribution function [GDP] of the random variable Y. (iii) Use the probability density function (PDF) fy to compute E[Y], Vor'), and the moment generating function qty/(t), where t 6 IR. (iv) Use the moment generating function qty to compute E[Y] and Vor(Y). c. {3 points) Let Z be a normal random variable with mean 5 and variance 4 [i.e., Z w N{:5,4}). (i) Use Table 2.3, page 76 in the text, to determine the probability P{3.52 5 Z S 9.14}. Explain. (ii) Dene the random variable 2' = 3.3 7. Specify the distribution of 2'. Explain