Question: Let Y 1 , Y 2 , . . . , Y n be a random sample of size n from the pdf f Y

Let Y1, Y2, . . . , Yn be a random sample of size n from the pdf fY(y; θ) = 1 θ e−y/θ, y > 0.

(a) Show that ˆθ1 = Y1, ˆθ2 = Y, and ˆθ3 = n・ Ymin are all unbiased estimators for θ.

(b) Find the variances of ˆθ1, ˆθ2, and ˆθ3.

(c) Calculate the relative efficiencies of ˆθ1 to ˆθ3 and ˆθ2 to ˆθ3.

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