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Let X1,..., Xn be a random sample from a distribution. Suppose Ti (X),T2(X) and U(X) respectively are sufficient, minimal sufficient, and unbiased estimators for the parameter θ of the distribution. Let U1(X) = E U(X) T, (X), U2(X) = EU㈤ T2(X)] a. Show that U1(X) and U(X) are unbiased for θ. b. Show that U2(x)-E[Uj(X)ITLX] c. Show that U2 has a smaller variance than U

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for 1:1,2- So UI() is unbiasad estimator db all mumi nal antftcient tatistic areb) All minimal nutficent ahiofic all rufficeut ntatisthc arte not minimal ALA fficial daなstic -02 CX) gmeratod buy Ti0x) ondE(x12) fram (b)

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