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Consider Poisson distribution f(x|θ) = (e^−θ) [(θ^x) / (x!)] for x = 0, 1, 2, ....

Consider Poisson distribution f(x|θ) = (e^−θ) [(θ^x) / (x!)] for x = 0, 1, 2, . . .

Let the prior distribution for θ be f(θ) = e^−θ for θ > 0.

(a) Show that the posterior distribution is a Gamma distribution. With what parameters?

(b) Find the Bayes’ estimator for θ.

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