Exercise 6. Let 0> 0 and XU[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 0 is unknown, but we can observe X. For given Oo, we want to test the hypothesis H: 020 against the alternative H₁: 0 < 0o. Consider the test which rejects Ho, if and only if X < c. dow 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 XU[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 0 is unknown, but we can observe X. For given Oo, we want to test the hypothesis H: 020 against the alternative H₁: 0 < 0o. Consider the test which rejects Ho, if and only if X < c. dow should we choose c, as a function of 0o and a, to get a test with significance level a? Carefully justify your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Exercise 6. Let 0> 0 and XU[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 00, we want to test the
hypothesis H: 020 against the alternative H₁: 0 < 0o. Consider the test which rejects
Ho, if and only if X < c. dow 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%2Fed029406-a1c1-473f-a3a0-6fd0fbd8e89d%2Fc51c0e66-83e0-4438-819f-104836bf664d%2Ft7rf1a9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 6. Let 0> 0 and XU[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 00, we want to test the
hypothesis H: 020 against the alternative H₁: 0 < 0o. Consider the test which rejects
Ho, if and only if X < c. dow 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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