Let X 1 , X 2 , , X n be a random sample of size n from the Poisson distribution, p X (k ) e k k , k 0, 1, Show that X i is an efficient estimator for

Question: Let X 1 , X 2 , . . . , X n be a random sample of size n from the Poisson distribution, p

Let X₁, X₂, . . . , X_n be a random sample of size n from the Poisson distribution, p_X(k; λ) = e^−λλ^k/k!, k = 0, 1, . . .. Show that ˆλ = Let X1, X2, . . . , Xn be a random sample X_i is an efficient estimator for λ.

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