Let X Exp() and Y Exp() be independent random variables. Let t > 0. Let A be the event that X t. (a) Find P(A B). (That is, find the change that X t). You may leave powers of e in your answer. (b) Are A and B independent? (That is, do we have P(AB) = P(A)P(B)?) You may use the fact that if T = min(X, Y ), then T Exp( + ), proved in the book in Example 6.34. You may also use the formula proved in 6.33 for P(X

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P( X