Question: If X1 X2 Xn constitute a
If X1, X2, . . . , Xn constitute a random sample from a population with the mean µ, what condition must be imposed on the constants a1, a2, . . . , an so that a1X1 + a2X2 + · · · + anXn is an unbiased estimator of µ?
Answer to relevant QuestionsIf X1, X2, . . . , Xn constitute a random sample from a normal population with µ = 0, show that Is an unbiased estimator of σ2. If Θ1 and Θ2 are independent unbiased estimators of a given parameter θ and var(Θ1) = 3 ∙ var(Θ2), find the constants a1 and a2 such that a1Θ1 + a2Θ2 is an unbiased estimator with minimum variance for such a linear ...If 1 and 2 are the means of independent random samples of sizes n1 and n2 from a normal population with the mean µ and the variance σ2, show that the variance of the unbiased estimator Is a minimum when ω = n1 / n1 + ...Since the variances of the mean and the midrange are not affected if the same constant is added to each observation, we can determine these variances for random samples of size 3 from the uniform population By referring ...To show that an estimator can be consistent with-out being unbiased or even asymptotically unbiased, consider the following estimation procedure: To estimate the mean of a population with the finite variance σ2, we first ...
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