Let X1, X2,..., Xn be independent and identically distributed exponential random variables. Show that the probability that the largest of them is greater than the sum of the others is n/2n−1. That is, if M = max j

X j then show P



M > n i=1 Xi − M



= n 2n−1 Hint: What is P{X1 > n i=2 Xi}?