Homework Help is Here – Start Your Trial Now!
Math
Statistics
Independent observations X₁, X₂ and X, come from normal distributions that have the same mean, μ, but whose variances are 3,2 and 4 respectively, so that X₁~ N(1, 3), X₂~ N(μ, 2), X₂~ N(µ,4). One possible estimator of μ is P₁ = (2X₁ +5X₂+4Xg). (a) Show that is an unbiased estimator of . (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 μ. Given that the variance of ₂ is 1, which of the estimators , and 2, is the better estimator of μ? Justify your answer.

Independent observations X₁, X₂ and X, come from normal distributions that have the same mean, μ, but whose variances are 3,2 and 4 respectively, so that X₁~ N(1, 3), X₂~ N(μ, 2), X₂~ N(µ,4). One possible estimator of μ is P₁ = (2X₁ +5X₂+4Xg). (a) Show that is an unbiased estimator of . (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 μ. Given that the variance of ₂ is 1, which of the estimators , and 2, is the better estimator of μ? Justify your answer.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 8E
See similar textbooks
icon
Related questions
Question

Q6 (example)

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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
SEE MORE TEXTBOOKS