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Suppose that Y has a Poisson distribution, P(Y = k) = e-λλk/ k!, k = 0, 1,... . Suppose Y can be observed only when Y ≥ 1, and we have no other information about λ. The problem is to estimate e-λ. Let V be an unbiased estimator of e-λ, so that V (k) is defined for k = 1, 2,..., with J,k≥1 e- λλk V (k)/(k!(1 - e -λ)) = e -λ, for all λ > 0. Solve, if possible, for the V (k) and comment on the properties and usefulness of the resulting estimator.

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