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.

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
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
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS