Y1, Y2, ... Yn are a random sample from the Gamma distribution with parameters α and β

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Y1, Y2, ... Yn are a random sample from the Gamma distribution with parameters α and β

(a) Suppose that α-4 is known and β is unknown. Find a complete sufficient statistic for β. Find the MVUE of β. (Hint: What is E(Y)?)

(b) Suppose that β = 4 is known and a is unknown. Find a complete sufficient statistic for α.

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