Let X1, X2, , Xn be Poisson random variables with parameter Assume that has an exponential distribution with 1 prior (a) Compute the posterior distribution of l and show that it is Gamma (b) Find the Bayes estimate of (( ixit 1 ), (n 1 ))

Question: Let X1, X2, . . ., Xn be Poisson random variables with parameter . Assume that has an exponential distribution with = 1

Let X1, X2, . . ., Xn be Poisson random variables with parameter Î». Assume that Î» has an exponential with Î¸ = 1 prior.
(a) Compute the posterior of l and show that it is Gamma

(b) Find the Bayes estimate of Î».

((-ixit 1 ), (n + 1 )).

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