Question 3. [10 Marks] (a) Let Xo, X1, X2, . . . be independent and identically distributed continuous random vari- ables with probability density function f(x). Let N be the first index k such that Xk > Xo. That is, N = 1 if X1 > Xo, N = 2 if X1 Xo, and so on. (i) Determine the probability mass function of N. (ii) Determine E(N). (iii) Explain how your answer would change if the random variables Xo, X1, ... were discrete rather than continuous. (b) Suppose X is distributed according to a Poisson distribution with mean parameter 1. The parameter A is itself a random variable with probability density function Ba g ( 1; a, B ) = 1"-exp(-BA), 1, a, B > O. Find the distribution of X. Calculate E[X ] and Var[X]