Consider a random sample X 1 , X 2 , , X n from the Poisson distribution with mean If the prior distribution for is a gamma distribution with hyperparameters 0 and 0 , show that the posterior distribution is also gamma distributed What are its hyperparameters ...

To show that the posterior distribution is also gamma distributed we can make use of the properties ...

Consider a random sample X 1 , X 2 , , X n from the Poisson distribution

Question:

Consider a random sample X₁, X₂, …, X_nfrom the Poisson distribution with mean µ. If the prior distribution for µ is a gamma distribution with hyperparameters α₀and β₀, show that the posterior distribution is also gamma distributed. What are its hyperparameters?

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