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[All Steps] Suppose X 1 , X 2 , ..., X n is a random sample of size a drawn from a Poisson pdf, where λ is an unknown parameter. Show that λ

Question: Suppose X 1 , X 2 , ..., X n is a random sample of size a drawn from a Poisson pdf, where \(\lambda \) is an unknown parameter. Show that \(\hat{\lambda }=\bar{X}\) is unbiased for \(\mu \). For what type of parameter, in general, will the sample mean necessarily be an unbiased estimator? Hint: The answer is implicit in the derivation showing that X is unbiased for the Poisson A.

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