In a game, the probability that player A wins on her rth go can be described as

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In a game, the probability that player A wins on her rth go can be described as a discrete random variable X, with probability function P(X = r) = 1/2r, for r = 1, 2, 3, ….

a. Find the probability generating function.

b. Find E(X) and Var(X).

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