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Let 01 (X) and 02(X) be two different and independent unbiased estimators of 0. Consider a number a E R. Let us now introduce an estimator given by a linear combination of the other two, namely Ôg(X) := aô, (X) + (1 – a)ê,(X). Select all correct statements. (Note that selection of incorrect options may attract small penalties.) Select one or more: O a. The mean of 03(X) is equal to 0. O b. The mean of 03 (X) is equal to að. O c. 03(X) is a biased estimator of 0. Od. Suppose that Var (ô,(X)) = can choose the constant a such that the mean squared error of 03(X) is 0(2n–1) n2 and Varo(@ (X)) = ; 202 Then we п-1 62(2n–1) equal to The mean squared error (MSE) of 03 (X) is always strictly larger than the MSE of the other two estimators O f. 03(X) is an unbiased estimator of 0.

Let 01 (X) and 02(X) be two different and independent unbiased estimators of 0. Consider a number a E R. Let us now introduce an estimator given by a linear combination of the other two, namely Ôg(X) := aô, (X) + (1 – a)ê,(X). Select all correct statements. (Note that selection of incorrect options may attract small penalties.) Select one or more: O a. The mean of 03(X) is equal to 0. O b. The mean of 03 (X) is equal to að. O c. 03(X) is a biased estimator of 0. Od. Suppose that Var (ô,(X)) = can choose the constant a such that the mean squared error of 03(X) is 0(2n–1) n2 and Varo(@ (X)) = ; 202 Then we п-1 62(2n–1) equal to The mean squared error (MSE) of 03 (X) is always strictly larger than the MSE of the other two estimators O f. 03(X) is an unbiased estimator of 0.

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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choose correct options..hand written plz
Let 01 (X) and 02(X) be two different and independent unbiased estimators of 0. Consider a number a E R. Let us now introduce an estimator given by a linear combination of the other two, namely Ôg(X) := aô, (X) + (1 – a)ê,(X). Select all correct statements. (Note that selection of incorrect options may attract small penalties.) Select one or more: O a. The mean of 03 (X) is equal to 0. . O b. The mean of 03 (X) is equal to að. O c. 03(X) is a biased estimator of 0. Od. Suppose that Var (ô,(X)) = can choose the constant a such that the mean squared error of 03(X) is e2(2n–1) n2 and Varo(@ (X)) = ; 202 Then we п-1 62(2n–1) equal to The mean squared error (MSE) of 03 (X) is always strictly larger than the MSE of the other two estimators O f. 03(X) is an unbiased estimator of 0.
Transcribed Image Text:Let 01 (X) and 02(X) be two different and independent unbiased estimators of 0. Consider a number a E R. Let us now introduce an estimator given by a linear combination of the other two, namely Ôg(X) := aô, (X) + (1 – a)ê,(X). Select all correct statements. (Note that selection of incorrect options may attract small penalties.) Select one or more: O a. The mean of 03 (X) is equal to 0. . O b. The mean of 03 (X) is equal to að. O c. 03(X) is a biased estimator of 0. Od. Suppose that Var (ô,(X)) = can choose the constant a such that the mean squared error of 03(X) is e2(2n–1) n2 and Varo(@ (X)) = ; 202 Then we п-1 62(2n–1) equal to The mean squared error (MSE) of 03 (X) is always strictly larger than the MSE of the other two estimators O f. 03(X) is an unbiased estimator of 0.
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