Question: If N is a geometric random variable with P (N = n) = (1/2)^n for n = 1, 2, . . ., and the (Xi)

If N is a geometric random variable with P (N = n) = (1/2)^n for n = 1, 2, . . ., and the (Xi) for i = 1, 2, . . . are independent Bernoulli type random variables with P (Xi = 1) = P (Xi = 1) = 1/2 for all i, find the generating function for S = X1 + + XN ; i.e. find E [t^S] and confirm that this is 1 when t = 1.

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