13. Let X1, X2,... be a sequence of independent random variables. The nonnegative integer valued random variable N is said to be a stopping time for the sequence if the event {N = n} is independent of Xn+1,Xn+2,... . The idea being that the Xi are observed one at a time—first X1, then X2, and so on—and N represents the number observed when we stop. Hence, the event {N = n} corresponds to stopping after having observed X1,...,Xn and thus must be independent of the values of random variables yet to come, namely, Xn+1,Xn+2,... .

(a) Let X1,X2,... be independent with