dependent observations X₁, X2 and X3 come from normal stributions that have the same mean, μ, but whose variances are 3,2 d 4 respectively, so that X₁~ N(μ, 3), X₂~ N(1,2), X₂~ N(μ, 4). ne possible estimator of μ is P₁ = (2X₁ +5X₂+4Xg). Show that is an unbiased estimator of μ. What is the variance of f₁? Carefully explain your workings and reasonings. The estimator A₂ = (X₁ + X₂ + X₂) is also an unbiased estimator of μ. Given that the variance of ₂ is 1, which of the estimators and 2, is the better estimator of μ? Justify your answer.
dependent observations X₁, X2 and X3 come from normal stributions that have the same mean, μ, but whose variances are 3,2 d 4 respectively, so that X₁~ N(μ, 3), X₂~ N(1,2), X₂~ N(μ, 4). ne possible estimator of μ is P₁ = (2X₁ +5X₂+4Xg). Show that is an unbiased estimator of μ. What is the variance of f₁? Carefully explain your workings and reasonings. The estimator A₂ = (X₁ + X₂ + X₂) is also an unbiased estimator of μ. Given that the variance of ₂ is 1, which of the estimators and 2, is the better estimator of μ? Justify your answer.
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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Transcribed Image Text:Independent observations X₁, X₂ and X3 come from normal
distributions that have the same mean, μ, but whose variances are 3,2
and 4 respectively, so that
X₁ ~ N(3),
X₂
~ N(µ, 2),
X₂ ~ N(1, 2), X3~ N(µ,4).
One possible estimator of μ is
P₁ = (2X₁ +5X₂ + 4Xg).
(a) Show that is an unbiased estimator of μ.
(b) What is the variance of ? Carefully explain your workings and
reasonings.
(c) The estimator
A2 = (X₁ + X₂ + X₂)
is also an unbiased estimator of u. Given that the variance of ₂
is 1, which of the estimators and 2, is the better estimator
of μ? Justify your answer.
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