Suppose that X1, . . . , Xn form a random sample from the Poisson distribution with

Question:

Suppose that X1, . . . , Xn form a random sample from the Poisson with unknown mean θ, and let
a. Determine the value of a constant c such that the estimator e−cY is an unbiased estimator of e−θ.
b. Use the information inequality to obtain a lower bound for the variance of the unbiased estimator found in part (a).
Distribution
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