reasonable estimator of 0.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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.
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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