The Poisson distribution is defined as: xke-x P(X = k) = k! - (k = 0, 1, 2, ...). (a) Let X1 ~ Poisson(A), and x be an observed value of X. What is the likelihood given X? [2 pts] Poisson (X) where X1, ..., Xn are i.i.d. random variables, and x1, ..., xn be observed values of X1, ..., Xn. What is the likelihood of this data (b) Now, assume we are given n such values. Let (X1, ..., Xn) given A? You may leave your answer in product form. [3 pts] (c) What is the maximum likelihood estimator of X? [10 pts] ~