Ononot — In a Bayesian hierarchical model, given a Poisson likelihood

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Inferential Statisticshard

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In a Bayesian hierarchical model, given a Poisson likelihood $X|\lambda \sim \text{Poisson}(\lambda)$ and a Gamma prior $\lambda \sim \text{Gamma}(\alpha, \beta)$ , what is the posterior distribution $\pi(\lambda|x)$ ?