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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

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 1 Consider three independent random variables x1, x2 and x3 with the same expected value u and variances 1/8, 1 and 4, respectively. Consider, also, two estimators 01 and 02 defined as 1 x3 + x2 2 1 and = 2x1 – x2. Choose the best answer: A) Both 01 and ô2 B) Both 0, and 02 are unbiased for u but 02 is more efficient C) Both 01 and 02 are biased for u D) Both 01 and 02 are unbiased for u but 03 = x2 is preferable to both are unbiased for u and they are equally efficient Question 2 Consider 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) = 0.5µ and V(ât) = o². Which statement is correct? A) The estimator aT is not consistent but 2âr is B) The estimator âr is consistent because its variance goes to zero C) We cannot determine whether the estimator âT is consistent with this information D) The estimator 2âr is unbiased but inconsistent
Transcribed Image Text:Question 1 Consider three independent random variables x1, x2 and x3 with the same expected value u and variances 1/8, 1 and 4, respectively. Consider, also, two estimators 01 and 02 defined as 1 x3 + x2 2 1 and = 2x1 – x2. Choose the best answer: A) Both 01 and ô2 B) Both 0, and 02 are unbiased for u but 02 is more efficient C) Both 01 and 02 are biased for u D) Both 01 and 02 are unbiased for u but 03 = x2 is preferable to both are unbiased for u and they are equally efficient Question 2 Consider 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) = 0.5µ and V(ât) = o². Which statement is correct? A) The estimator aT is not consistent but 2âr is B) The estimator âr is consistent because its variance goes to zero C) We cannot determine whether the estimator âT is consistent with this information D) The estimator 2âr is unbiased but inconsistent
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