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Let Y1, ..., Yn be IID Poisson(λ) random variables. Argue that Y¯ , the sample mean,...

Let Y1, ..., Yn be IID Poisson(λ) random variables. Argue that Y¯ , the sample mean, is a sufficient statistic for λ by using the factorization criterion. Assuming that Y¯ is a complete sufficient statistic, explain why Y¯ is the minimum variance unbiased estimator.

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