Examine whether as an estimator of a a is 1 unbiased 2, Engineering Mathematics

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Examine whether as an estimator of a a is 1 unbiased 2

Question: Suppose that is an estimator of a derived from a sample of size T. We are given that

E(α^) = α + 2/T and var(α^) = 4α/T + α²/T²

(a) Examine whether as an estimator of α, α^ is (1) unbiased, (2) consistent, (3) asymptotically unbiased, and (4) asymptotically efficient.

(b) What is the asymptotic variance of α^?

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Engineering Mathematics: Examine whether as an estimator of a a is 1 unbiased 2

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