where X0 := oo. Suppose you have generated I: such random variables. Find the probability that the record occurs at time k, i.e., P{Xk > X1.Xk > X2,...,X1c > Xk_1}. (Hint: The events {JGc > X1}, {Xk > X2},... are not independent! T hink about conditioning and utilize Problem 2(a) in HW#1.) Note: Intuitively, since all Xg's are i.i.d., it is equally likely that any of them (or in particular, X k) is the largest one, so the probability should be l/k. In fact, this answer is correct, but the argument here is entirely based on non-rigorous intuition. Here, you will prove this using mathematical steps via conditioning