Question: If (x1, . . ., xn) is a sample from a Poisson (0) distribution, where e E (0,00) is unknown, then determine the MLE of

If (x1, . . ., xn) is a sample from a

If (x1, . . ., xn) is a sample from a Poisson (0) distribution, where e E (0,00) is unknown, then determine the MLE of 0. (b) Show that ER X; is sufficient for e. (c) Evaluate the mean and variance of the maximum likelihood estimator for 0. (d) What is the MLE for 02? Is it unbiased? If not, what is its bias? (e) What is the MLE for Po(X, = 0)? Hint: what function of the parameter is this proba- bility

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