Let X11 X12X1, and X21, X22X2nz be two independent random samples of size ni and n₂ from two normal populations N(₁, 2) and N(2, 2) respectively. (a) Derive the maximum likelihood estimators (mle's) of all the parameters in the first population (X₁). Using analogy, state the mle's of the parameters of the second population. (b) Find the pooled estimator of the common variance when it is assumed that of = o=0². Suggest an unbiased estimator of o². (c) Assuming both ny and n₂ are small, suggest a pivotal function that can be used to derive a (1-a) x 100% confidence interval for (₁-₂) when o² = 0₂ = 0².
Let X11 X12X1, and X21, X22X2nz be two independent random samples of size ni and n₂ from two normal populations N(₁, 2) and N(2, 2) respectively. (a) Derive the maximum likelihood estimators (mle's) of all the parameters in the first population (X₁). Using analogy, state the mle's of the parameters of the second population. (b) Find the pooled estimator of the common variance when it is assumed that of = o=0². Suggest an unbiased estimator of o². (c) Assuming both ny and n₂ are small, suggest a pivotal function that can be used to derive a (1-a) x 100% confidence interval for (₁-₂) when o² = 0₂ = 0².
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:Let X₁1 X12X1, and X21, X22X22 be two independent random samples of
size ni and n₂ from two normal populations N(₁, 2) and N(2, 2) respectively.
(a) Derive the maximum likelihood estimators (mle's) of all the parameters in the first
population (X₁). Using analogy, state the mle's of the parameters of the second
population.
(b) Find the pooled estimator of the common variance when it is assumed that of =
=o². Suggest an unbiased estimator of o².
(c) Assuming both ny and n₂ are small, suggest a pivotal function that can be used to
derive a (1-a) x 100% confidence interval for (₁-₂) when of = 0 = 0².
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Write the given information.
VIEWStep 2: Derive the maximum likelihood estimators for the population mean(X1).
VIEWStep 3: Derive the maximum likelihood estimators for the population variance.
VIEWStep 4: Determine the pooled estimator of the common variance.
VIEWStep 5: Derive (1 - α)*100% confidence interval for the population mean difference.
VIEWSolution
VIEW
Step by step
Solved in 6 steps with 20 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman