Question: Consider a random sample X 1 , . . ., X n from an exponential distribution with parameter , and assign to a Gamma(

Consider a random sample X₁, . . ., X_nfrom an exponential distribution with parameter λ, and assign to λ a Gamma(α₀, β₀) prior distribution.
a. What is the prior expectation of λ?
b. Determine the Bayes estimator λ̃.

c. Let λ* denote the true value of λ. Show that ^k is a consistent estimator of λ*.

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