Consider a random sample of size one (n 1) from the distribution with probabilityfunctionf(y; 0) =Joy(-1), if 0 010.otherwise.(a) To test Ho: 0 = 0o versus H₁ : 0 = 0 > 00, find a most powerful test. Let thepositive constant to define the rejection region of the test be k.(d) Graph the power function against for k=0.3, 0.5, 0.8, and comment on how thepower of the test changes as the values of k and change.(e) Is the above test in part (a) a uniformly most powerful test? Justify your answer.

Answered: Image /qna-images/answer/27d5aa20-e2fd-482e-bb46-2f0a02aba715.jpg

Answered: Consider a random sample of size one…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Consider a random sample of size one (n 1) from the distribution with probability function Soy(-1), if 00 f(y; 0)= 10. otherwise. (a) To test Ho: 0 = 0o versus H₁ : 0 = 0 > 00, find a most powerful test. Let the positive constant to define the rejection region of the test be k. (d) Graph the power function against for k= 0.3, 0.5, 0.8, and comment on how the power of the test changes as the values of k and change. (e) Is the above test in part (a) a uniformly most powerful test? Justify your answer.
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