5. The random observation X follows a binomial distribution, say B(n,x). A second, independent, random observation Y follows B(m, ty). Further we have the following set of hypotheses, H₁ : x = y against H₁ : ¹x ‡ ¹y. (a) Write down the joint likelihood under both hypotheses in (1). (1) (b) Find the maximum likelihood estimators of the unknown parameters and the corresponding maximized likelihoods under both hypotheses in (1). (c) Find the critical region of significance level a for testing (1), the test statistic and its asymptotic distribution for large values of n and m.
5. The random observation X follows a binomial distribution, say B(n,x). A second, independent, random observation Y follows B(m, ty). Further we have the following set of hypotheses, H₁ : x = y against H₁ : ¹x ‡ ¹y. (a) Write down the joint likelihood under both hypotheses in (1). (1) (b) Find the maximum likelihood estimators of the unknown parameters and the corresponding maximized likelihoods under both hypotheses in (1). (c) Find the critical region of significance level a for testing (1), the test statistic and its asymptotic distribution for large values of n and m.
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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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!
Transcribed Image Text:5. The random observation X follows a binomial distribution, say B(n,x).
A second, independent, random observation Y follows B(m, ây).
Further we have the following set of hypotheses,
Ho : x = ¹y against H₁ : πx ‡ ¹y.
(a) Write down the joint likelihood under both hypotheses in (1).
(1)
(b) Find the maximum likelihood estimators of the unknown
parameters and the corresponding maximized likelihoods under
both hypotheses in (1).
(c) Find the critical region of significance level a for testing (1), the
test statistic and its asymptotic distribution for large values of n
and m.
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