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a Derive the likelihood function L(0) as a function of N, N2, and Ng. b Find the most powerful test for testing Ho:0 = 6 versus H,:0 = 0, where 0, > 6o. Show that your test specifies that H be rejected for certain values of 2N+ N2. c How do you determine the value of k so that the test has nominal level a? You need not do %3D the actual computation. A clear description of how to determine k is adequate.

a Derive the likelihood function L(0) as a function of N, N2, and Ng. b Find the most powerful test for testing Ho:0 = 6 versus H,:0 = 0, where 0, > 6o. Show that your test specifies that H be rejected for certain values of 2N+ N2. c How do you determine the value of k so that the test has nominal level a? You need not do %3D the actual computation. A clear description of how to determine k is adequate.

A First Course in Probability (10th Edition)
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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Let Y, Y2,.. Y, be independent and identically distributed random variables with discrete probability function given by 3 p(y 0) 02 20(1 – 0) (1-0)² where 0 < 0 < 1. Let N; denote the number of observations equal to i for i = 1, 2, 3. Hypothesis Testing a Derive the likelihood function L(6) as a function of N1, N2, and N3. b Find the most powerful test for testing Ho:0 = 00 versus H.:0 = 0, where 0, > 6o. Show that your test specifies that H, be rejected for certain values of 2N, + N2. c How do you determine the value of k so that the test has nominal level a? You need not do the actual computation. A clear description of how to determine k is adequate.
Transcribed Image Text:Let Y, Y2,.. Y, be independent and identically distributed random variables with discrete probability function given by 3 p(y 0) 02 20(1 – 0) (1-0)² where 0 < 0 < 1. Let N; denote the number of observations equal to i for i = 1, 2, 3. Hypothesis Testing a Derive the likelihood function L(6) as a function of N1, N2, and N3. b Find the most powerful test for testing Ho:0 = 00 versus H.:0 = 0, where 0, > 6o. Show that your test specifies that H, be rejected for certain values of 2N, + N2. c How do you determine the value of k so that the test has nominal level a? You need not do the actual computation. A clear description of how to determine k is adequate.
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