A single observation of a random variable havinga geometric distribution is to be used to test the null hypothesis that its parameter equals θ0 against the alter-native that it equals θ1 > θ0. Use the Neyman–Pearson lemma to find the best critical region of size α.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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A single observation of a random variable having
a geometric distribution is to be used to test the null

hypothesis that its parameter equals θ0 against the alter-
native that it equals θ1 > θ0. Use the Neyman–Pearson

lemma to find the best critical region of size α.

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