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Consider three boxes and n marbles. For each marble, I will randomly put it into box i with probability p; for i = 1, 2, 3. Suppose that there are Y₁, Y3, Y3 marbles in the three boxes. Find a LRT statistic to test the hypothesis Ho p₁ = p2 = p3 V.S. H₁: Ho is false. Find the asymptotic size a LRT test.

Consider three boxes and n marbles. For each marble, I will randomly put it into box i with probability p; for i = 1, 2, 3. Suppose that there are Y₁, Y3, Y3 marbles in the three boxes. Find a LRT statistic to test the hypothesis Ho p₁ = p2 = p3 V.S. H₁: Ho is false. Find the asymptotic size a LRT test.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 24E
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Consider three boxes and n marbles. For each marble, I will randomly put it into box i with probability p; for i = 1, 2, 3. Suppose that there are Y₁, Y3, Y3 marbles in the three boxes. Find a LRT statistic to test the hypothesis Ho p₁ = p2 = p3 V.S. H₁: Ho is false. Find the asymptotic size a LRT test.
Transcribed Image Text:Consider three boxes and n marbles. For each marble, I will randomly put it into box i with probability p; for i = 1, 2, 3. Suppose that there are Y₁, Y3, Y3 marbles in the three boxes. Find a LRT statistic to test the hypothesis Ho p₁ = p2 = p3 V.S. H₁: Ho is false. Find the asymptotic size a LRT test.
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