Let X 1 ,X 2 , ,X n be a random sample from a distribution with pdf f(x ) 2 xe x , 0 x , where 0 (a) Argue that Y n 1 Xi is a complete sufficient statistic for (b) Compute E(1 Y ) and find the function of Y which is the unique MVUE of

Question: Let X 1 ,X 2 , . . .,X n be a random sample from a distribution with pdf f(x; ) = 2 xe

Let X₁,X₂, . . .,X_n be a random sample from a distribution with pdf f(x; θ) = θ²xe^−θx, 0 < x < ∞, where θ > 0.
(a) Argue that Y = Σⁿ₁ Xi is a complete sufficient statistic for θ.
(b) Compute E(1/Y ) and find the function of Y which is the unique MVUE of θ.

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