6. Suppose the common pmf of the random sample X₁, X₂, ..., X, is Poisson with unknown parameter > 0, with pmf: -0 0 e " x! x = 0, 1, 2, Suppose also that the prior distribution of the parameter 0 is gamma with pdf: a-1 -- e a > 0, λ > 0. f(x|0) = 1 г(α)λª ƒ(0|a, λ) = - " A (a) Find a Bayesian Estimator (BE) 0 of 0. B ^ (b) Express from part (a) as a function of the sample mean X and the mean λ of 0. B

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