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4. Let X₁, X2, Xn represent a random sample from a distribution with E(X) = 0. Consider two estimators of 0: 0 = X1 and 0₂ = X. (a) Show that both estimators ₁ and 2 are unbiased estimators of 0. (b) Let Var(X) = o², find Var(8₁) and Var(82) in terms of o². (c) Which of these estimators, ₁ or 02, is better? Justify your answer.

4. Let X₁, X2, Xn represent a random sample from a distribution with E(X) = 0. Consider two estimators of 0: 0 = X1 and 0₂ = X. (a) Show that both estimators ₁ and 2 are unbiased estimators of 0. (b) Let Var(X) = o², find Var(8₁) and Var(82) in terms of o². (c) Which of these estimators, ₁ or 02, is better? Justify your answer.

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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4. Let X₁, X2, Xn represent a random sample from a distribution with E(X) Consider two estimators of 0: ... 01 = X1 and Ông = X. (a) Show that both estimators ₁ and 2 are unbiased estimators of 0. (b) Let Var(X) = o², find Var(Ô₁) and Var(8₂) in terms of o². (c) Which of these estimators, ₁ or 02, is better? Justify your answer. = 0.
Transcribed Image Text:4. Let X₁, X2, Xn represent a random sample from a distribution with E(X) Consider two estimators of 0: ... 01 = X1 and Ông = X. (a) Show that both estimators ₁ and 2 are unbiased estimators of 0. (b) Let Var(X) = o², find Var(Ô₁) and Var(8₂) in terms of o². (c) Which of these estimators, ₁ or 02, is better? Justify your answer. = 0.
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