Question: 10. Referring to Problem 9, (a) Show that U = (n + 1)/n is unbiased for . (b) Find the variance of U. (c) Verify

10. Referring to Problem 9,

(a) Show that U = (n + 1)ˆθ/n is unbiased for θ.

(b) Find the variance of U.

(c) Verify that 2¯X is unbiased for θ. Find the variance of 2¯X .

(d) Determine the ratio V ar(U)/V ar(2¯X ). Which of the unbiased estimators would you prefer?

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