A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question
Let X₁, X₂, ‚X₂be i.i.d. with following probability mass function 0.1 +0, x = 1 x = 2 x = 3 S p(x 10) = 0.5, 0.4-0, where -0.1 ≤ 0 ≤ 0.4 1. Find a reasonable estimator of 0. 2. Suppose that n = 1, find a most powerful text (with level 0.1) for Ho: 0 = 0 versus HA: 0 = 0.3 3. Suppose that n = 1, and the test hypothesis is H : 0 = 0 versus H₁ : 0 > 0, does a uniformly most powerful test exist? If it exists, please find it.
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Transcribed Image Text:Let X₁, X₂, ‚X₂be i.i.d. with following probability mass function 0.1 +0, x = 1 x = 2 x = 3 S p(x 10) = 0.5, 0.4-0, where -0.1 ≤ 0 ≤ 0.4 1. Find a reasonable estimator of 0. 2. Suppose that n = 1, find a most powerful text (with level 0.1) for Ho: 0 = 0 versus HA: 0 = 0.3 3. Suppose that n = 1, and the test hypothesis is H : 0 = 0 versus H₁ : 0 > 0, does a uniformly most powerful test exist? If it exists, please find it.
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Step 1: Write what is given in the question.
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Step 2: Find reasonable estimator.
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Step 3: Find Most powerful test
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Step 4: Find UMP if exists .
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