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Competitive Stats
Q134Section III (Statistics)134 of 180

UMVUE of e−θe^{-\theta} for Poisson data — a binomial thinning argument

Suppose {X1,X2,…,Xn},n≥2\{X_1,X_2,\dots,X_n\}, n\ge2 is a random sample from Poisson distribution with mean θ\theta. If T=∑i=1nXiT=\sum_{i=1}^nX_i, then the MVUE of e−θe^{-\theta} is:

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