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Inferential Statisticshard
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Consider a Bayesian framework with a Poisson likelihood X∣λ∼Poisson(λ)X|\lambda \sim \text{Poisson}(\lambda)X∣λ∼Poisson(λ) and a Gamma prior λ∼Gamma(α,β)\lambda \sim \text{Gamma}(\alpha, \beta)λ∼Gamma(α,β). What is the form of the posterior distribution?