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Let {X1, ..., Xn} be i.i.d. from a distribution with pdf f(x; θ) = θ/xθ+1 for...

Let {X1, ..., Xn} be i.i.d. from a distribution with pdf f(x; θ) = θ/xθ+1 for θ > 2 and x > 1.

(a) (10 points) Calculate EX1 and V ar(X1).

(b) (5 points) Find the method of moments estimator of θ.

(c) (5 points) If we denote the method of moments estimator as ˆθ1. What does √ n( ˆθ1 − θ) converge in distribution to? (d) (5 points) Is the method of moment estimator efficient? Verify your answer.

Math   Statistics-And-Probability   
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