Question: Consider the Normal (two-parameter) statistical model. (a) Derive (not guess!) the sampling distributions of the following estimators: (i) = Xn, (ii) = (x1+x2+X3), (iii) 3=(X-X),

Consider the Normal (two-parameter) statistical model.

(a) Derive (not guess!) the sampling distributions of the following estimators:

(i) = Xn, (ii) = (x1+x2+X3), (iii) 3=(X-X), (iv) n = Xi

(i) = Xn, (ii) = (x1+x2+X3), (iii) 3=(X-X), (iv) n = Xi (HINT: State explicitly any properties of E(.) or any lemmas you use.) (b) Compare these estimators in terms of the optimal properties, unbiasedness, effi- ciency, and consistency. (c) Compare and contrast the estimators = (-n) and s (X) in terms of their properties. =

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