# Question

If X has a Poisson distribution and the prior distribution of its parameter Λ(capital Greek lambda) is a gamma distribution with the parameters α and β, show that

(a) The posterior distribution of given X = x is a gamma distribution with the parameters α + x and β / β + 1 ;

(b) The mean of the posterior distribution of Λ is

(a) The posterior distribution of given X = x is a gamma distribution with the parameters α + x and β / β + 1 ;

(b) The mean of the posterior distribution of Λ is

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