Let {X} be a sequence of i.i.d. continuous random variables with probability density function f(x). (a) Find P(X X). (b) Find P(X X2, X1 X3). (c) Let N be a new integer-valued random variable defined as follows. N is the index of the first random variable that is less than X, that is, P(N = n) = P(X X2, X X3,..., X Xn-1, X > Xn). Find P(N> n) as a function of n. (d) Show that E(N) = (5)