Question: 4.5. Suppose X₁, X₂, ..., 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.