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7. (15 pts) Let X1, ..., Xn be n independent samples from a Poisson random variable with parameter 1. Prove that Li 1 Xi is the most efficient unbiased estimator for 1. n (Recall that for a Poisson random variable, X, with parameter ), P(X = k) = \\kxk /k! for k E N and EX = > and Var(X) = >)