5. a) The amount of time that a certain type of component functions before failing is a [12 Marks] random variable with probability density function fx (x) = 20, 0 35) = 0.90. In other words, how many components would one need to have on hand to be approximately 90% certain that the stock would last at least 35 days? b) The random variables X and Y are bivariate normal, with joint moment generating function Mx.y (t1, (2) = exp 5 (ti+ 2t1 12 + 412) (i) Find E(X), E(Y), var(X), var(Y), cov (X, Y) and corr (X, Y). (ii) What is the distribution of Y given X = 1? Hence compute E (Y|X = 1) and var (Y|X = 1)