Let X1, . . . , Xn be iid from a Poisson distribution with unknown λ. Following the Bayesian paradigm, suppose we assume the prior distribution for λ is Gamma(α, β).
(a) Find the posterior distribution of λ.
(b) Is Gamma a conjugate prior? Explain.
(c) Use software or tables to provide a 95% credible interval for λ using the 2.5th percentile and 97.5th percentile in the case where xi = 13 and n=10, assuming α = 1 andβ = 1 for our prior. Interpret the interval.
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