Exercise 6. Let 0> 0 and X~U[0, 0], i.e. X is uniformly distributed on the interval [0,0]. a) As a function of 0, determine P(X ≤ 1). b) Assume that is unknown, but we can observe X. For given 0o, we want to test the hypothesis Ho: 0200 against the alternative H₁: 0 < 0o. Consider the test which rejects Ho, if and only if X < c. How should we choose c, as a function of 0o and a, to get a test with significance level a? Carefully justify your answer.
Exercise 6. Let 0> 0 and X~U[0, 0], i.e. X is uniformly distributed on the interval [0,0]. a) As a function of 0, determine P(X ≤ 1). b) Assume that is unknown, but we can observe X. For given 0o, we want to test the hypothesis Ho: 0200 against the alternative H₁: 0 < 0o. Consider the test which rejects Ho, if and only if X < c. How should we choose c, as a function of 0o and a, to get a test with significance level a? Carefully justify your answer.
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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![Exercise 6. Let 0> 0 and X~U[0,0], i.e. X is uniformly distributed on the interval [0,0].
a) As a function of 0, determine P(X ≤ 1).
b) Assume that is unknown, but we can observe X. For given 0o, we want to test the
hypothesis Ho: 0 ≥ 00 against the alternative H₁: 0 < 0o. Consider the test which rejects
Ho, if and only if X < c. How should we choose c, as a function of 0o and a, to get a test
with significance level a? Carefully justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4061eb31-6ba2-4539-9b51-dd7b05481e7e%2Ffe1a6ae8-3f28-4ae7-9b02-8109d40821a2%2Fxo10wa8_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 6. Let 0> 0 and X~U[0,0], i.e. X is uniformly distributed on the interval [0,0].
a) As a function of 0, determine P(X ≤ 1).
b) Assume that is unknown, but we can observe X. For given 0o, we want to test the
hypothesis Ho: 0 ≥ 00 against the alternative H₁: 0 < 0o. Consider the test which rejects
Ho, if and only if X < c. How should we choose c, as a function of 0o and a, to get a test
with significance level a? Carefully justify your answer.
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