5.12 A discrete random variable with probabilities P(X = x) = a(x) x /C(), x = 0,...

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5.12 A discrete random variable with probabilities P(X = x) = a(x)θ x /C(θ), x = 0, 1,... ; a(x) ≥ 0; θ > 0, is a power series distribution. This is an exponential family (5.1) with s = 1, η = log θ, and T = X. The moment generating function is MX(u) = C(θeu)/C(θ).

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