Exercise 3.7Bayesian analysis of the Poisson distribution In Exercise 3.6, we defined the Poisson distribution with rate?and derived its MLE. Here we perform a conjugate Bayesian analysis. a. Derive...

Exercise 3.7Bayesian analysis of the Poisson distribution

In Exercise 3.6, we defined the Poisson distribution with rate?and derived its MLE. Here we perform a conjugate Bayesian analysis.

a. Derive the posteriorp(?|D)assuming a conjugate priorp(?) = Ga(?|a,b)??a-1e-?b. Hint: the posterior is also a Gamma distribution.

b. What does the posterior mean tend to asa?0andb?0? (Recall that the mean of aGa(a, b) distribution isa/b.)