Consider the simple Poisson model based on f (x; ) = xe /x!, >0, x = 0,
Question:
Consider the simple Poisson model based on f (x; θ) = θxeθ /x!, θ>0, x = 0, 1, 2, . . .
(a) Derive the Cramer–Rao lower bound for unbiased estimators of θ.
(b) Explain why X = 1n
ni
=1 Xi is an unbiased and fully efficient estimator of θ.
(c) Derive the posterior distribution when π(θ) is Gamma(α, β).
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