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Q19Section A (Section A)19 of 60

UMVUE of the square of a Poisson parameter

Let X1,…,XnX_1,…,X_n (n>1n>1) be a random sample from a Poisson(θ)Poisson(\theta) population, θ>0\theta>0, and T=∑i=1nXiT=\sum_{i=1}^nX_i. Then the uniformly minimum variance unbiased estimator of θ2\theta^2 is

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