Question: (Bayesian) Suppose that X is Poisson(λ + 1), and the prior distribution of λ is...

Question:

(Bayesian) Suppose that X is Poisson(λ + 1), and the prior distribution of λ is binomial(2,1/3).

(a) Find the Bayesian estimate of λ for mean square loss based on the single observation X, if X = 1.

(b) Find the Bayesian estimate of λ for mean square loss based on the single observation X, if X = 2

Hints:

Because of its prior distribution, λ can take only three values, 0,1,2.

Don’t expect its posterior distribution to be any distribution we have seen before;

You will have to compute (numerically) the posterior probabilities of the three possible values.

Solutions

Expert Solution

orchestra answered 1 year ago

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