Question: Let X1,..., Xn be iid n(θ, θ2), θ > 0. For this model both and cS are unbiased estimators of θ, where (a) Prove that

Let X1,..., Xn be iid n(θ, θ2), θ > 0. For this model both and cS are unbiased estimators of θ, where
Let X1,..., Xn be iid n(θ, θ2), θ > 0.

(a) Prove that for any number a the estimator a + (l - a)(cS) is an unbiased estimator of θ.
(b) Find the value of a that produces the estimator with minimum variance.
(c) Show that (, S2) is a sufficient statistic for θ but it is not a complete sufficient statistic.

Vn-Ir((n 1)/2) V2T(n/2)

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