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The mean of 03 (X) is equal to 0. O b. The mean of 03 (X) is equal to ab. O c. Ô3(X) is a biased estimator of 0. O d. Suppose that Var (§,(X)) 62(2n–1) n2 and Varo(02(X)) 202 Then we n-1 can choose the constant a such that the mean squared error of 03 (X) is 62(2n–1) equal to n2 J e. 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.

The mean of 03 (X) is equal to 0. O b. The mean of 03 (X) is equal to ab. O c. Ô3(X) is a biased estimator of 0. O d. Suppose that Var (§,(X)) 62(2n–1) n2 and Varo(02(X)) 202 Then we n-1 can choose the constant a such that the mean squared error of 03 (X) is 62(2n–1) equal to n2 J e. 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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
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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 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.
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 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.
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