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5. Let X₁, X2,..., Xn be iid N(A, A²), A > 0. For this model both X and cS are unbiased √n - II ((n − 1)/2) - estimators of X, where c = √21(n/2) a. Prove that for any number b the estimator bX+(1-b) (cS) is an unbiased estimator of X. b. Find the value of b that produces the estimator with minimum variance in part(a). c. Show that (X, S²) is a sufficient statistics for X.

5. Let X₁, X2,..., Xn be iid N(A, A²), A > 0. For this model both X and cS are unbiased √n - II ((n − 1)/2) - estimators of X, where c = √21(n/2) a. Prove that for any number b the estimator bX+(1-b) (cS) is an unbiased estimator of X. b. Find the value of b that produces the estimator with minimum variance in part(a). c. Show that (X, S²) is a sufficient statistics for X.

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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5. Let X₁, X2,..., Xn be iid N(X, A²), A > 0. For this model both X and cS are unbiased √n – II ((n − 1)/2) estimators of A, where c = √2T (n/2) a. Prove that for any number b the estimator bX+(1−b) (cS) is an unbiased estimator of X. b. Find the value of b that produces the estimator with minimum variance in part(a). c. Show that (X, S²) is a sufficient statistics for A.
Transcribed Image Text:5. Let X₁, X2,..., Xn be iid N(X, A²), A > 0. For this model both X and cS are unbiased √n – II ((n − 1)/2) estimators of A, where c = √2T (n/2) a. Prove that for any number b the estimator bX+(1−b) (cS) is an unbiased estimator of X. b. Find the value of b that produces the estimator with minimum variance in part(a). c. Show that (X, S²) is a sufficient statistics for A.
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