Let X1 and X2 be two observations on an iid random variable drawn from a population...

Let X₁ and X₂ be two observations on an iid random variable drawn from a population with mean μ and variance σ² (for example, the random variable could be income; X₁ could be person 1’s income and X₂, person 2’s income). Which of the following is an unbiased estimator of mean income?

All of these are unbiased estimators of mean income.

23X1+13X2

15X1+45X2

Which of the following is the “best” (that is, least-variance) estimator of mean income?

15X1+45X2

23X1+13X2

All of these are "best" estimators of mean income.

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orchestra answered 11 months ago

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