Consider a random sample X 1, . . ., X n from a Poisson distribution with unknown mean , and assign to Gamma( 0

Consider a random sample X_1, . . ., X_n from a Poisson distribution with unknown mean µ, and assign to µ Gamma(α₀, β₀) prior distribution.
a. What is the prior expectation of µ?
b. Determine the Bayes estimator µ̂.
c. Let µ* denote the true value of l. Show that ^l is a consistent estimator of µ̂.*