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Suppose Y1,··· ,Yn is a sample from a exponential distribution with mean θ, and let Y(1),···...

Suppose Y1,··· ,Yn is a sample from a exponential distribution with mean θ, and let Y(1),··· ,Y(n) denote the order statistics of the sample.

(a) Find the constant c so that cY(1) is an unbiased estimator of θ.
(b) Find the sufficient statistic for θ and MVUE for θ.

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