The Poisson distribution is defined as: (a) Let X₁ P(X= k) = ~ xke-x k! Poisson(A), and x₁ be an observed value of X₁. What is the likelihood given X? (b) Now, assume we are given n such values. Let (X₁,..., Xn) Poisson(X) where X₁,..., Xn are i.i.d. random variables, and x₁,..., n be observed values of X₁, ,..., Xn. What is the likelihood of this data given A? You may leave your answer in product form. (c) What is the maximum likelihood estimator of λ? -(k = 0, 1, 2, ...).

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