Question 1Consider three independent random variables x1, x2 and x3 with the same expected value u andvariances 1/8, 1 and 4, respectively. Consider, also, two estimators 01 and 02 defined as1x3 +x221and= 2x1 – x2.Choose the best answer:A) Both 01 and ô2B) Both 0, and 02 are unbiased for u but 02 is more efficientC) Both 01 and 02 are biased for uD) Both 01 and 02 are unbiased for u but 03 = x2 is preferable to bothare unbiased for u and they are equally efficientQuestion 2Consider a population with mean u and variance o? < oo. After collecting an IID sample of T ob-servations, you estimate the mean of the population with an estimator âr such that E(âT) = 0.5µand V(ât) = o². Which statement is correct?A) The estimator aT is not consistent but 2âr isB) The estimator âr is consistent because its variance goes to zeroC) We cannot determine whether the estimator âT is consistent with this informationD) The estimator 2âr is unbiased but inconsistent

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Consider three independent random variables x1, x2 and x3 with the same expected value µ and variances 1/8, 1 and 4, respectively. Consider, also, two estimators 01 and Ô2 defined as 1 1 L3 + T2 2 and = 2x1 – x2. Choose the best answer: A) Both 01 and 02 i B) Both Ô0, and 02 are unbiased for µ but 0, is more efficient C) Both 01 and 02 are biased for µ D) Both 01 and 02 are unbiased for µ but 03 = x2 is preferable to both are unbiased for u and they are equally efficient

Consider three independent random variables x1, x2 and x3 with the same expected value µ and variances 1/8, 1 and 4, respectively. Consider, also, two estimators 01 and Ô2 defined as 1 1 L3 + T2 2 and = 2x1 – x2. Choose the best answer: A) Both 01 and 02 i B) Both Ô0, and 02 are unbiased for µ but 0, is more efficient C) Both 01 and 02 are biased for µ D) Both 01 and 02 are unbiased for µ but 03 = x2 is preferable to both are unbiased for u and they are equally efficient

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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