(14pts) Let X and Y be i.i.d. geometric random variables with parameter (probability of success) p, 0 < p < 1. (a) (6pts) Find P(X > Y ). (b) (8pts) Find P(X + Y = n) and P(X = k∣X + Y = n), for n = 2, 3, ..., and k = 1, 2, ..., n − 1.
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