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Problem 0.2 Recall the Geometric(p) distribution where X-number of flips of a coin until you get a head (H) with Pr(H) -p. The distribution is Pr(X- (1-p)1p for 1,2,. , with mean E(X)x(1 - p)*-p- 1/p, which can be obtained by brute force. An easier way to find the mean is to condition on the first toss, say Y- 0or 1 if the first toss is T or H. Show the mean is 1/p using E(X) EE(X Y)

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