Question: Let X be a r.v. such that pj = P (X = j) > 0, j = 0, 1, 2, ... and j=0 pj =

Let X be a r.v. such that pj = P (X = j) > 0, j = 0, 1, 2, ... and j=0 pj = 1. Let g(s) be the pgf of X, i.e., g(s) = EsX . (a). Show that EX = g(1) and var(X) = g(1) + g(1) [g(1)]2. (b). By applying (a), show that if X P oisson(), where > 0, then EX = and var(X) =

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