10 points) Let X1; X2, X3, ... be a sequence of independent random variables, where X; is exponentially distributed with parameter 1 for all i 2 1. We define Sn = Xi for all n 2 1. i=1 (a) Does the sequence (") 1 converge as n - co with probability 1? What is the limiting value? Justify your answer, (b) Compute explicitly the limit lim P[S, En]. n-+00 Justify your reasoning carefully