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Let X₁, Xn be a random sample from the beta distribution with a = B = 0 and = = {0: 0= 1,2}. Show that the likelihood ratio test statistic for testing Ho: 0= 1 vs. H₁: 0 = 2 is a function of the statistic W = ₁ log X₁ + 1 log(1 - X₁). i=1

Let X₁, Xn be a random sample from the beta distribution with a = B = 0 and = = {0: 0= 1,2}. Show that the likelihood ratio test statistic for testing Ho: 0= 1 vs. H₁: 0 = 2 is a function of the statistic W = ₁ log X₁ + 1 log(1 - X₁). i=1

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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3. Let X₁,..., Xn be a random sample from the beta distribution with a = ß = 0 and N = {0: 0 = 1,2}. Show that the likelihood ratio test statistic for testing Ho: 0 = 1 vs. H₁: 0 = 2 is a function of the statistic W = ₁ log X₁ + ₁ log(1 — X₁).
Transcribed Image Text:3. Let X₁,..., Xn be a random sample from the beta distribution with a = ß = 0 and N = {0: 0 = 1,2}. Show that the likelihood ratio test statistic for testing Ho: 0 = 1 vs. H₁: 0 = 2 is a function of the statistic W = ₁ log X₁ + ₁ log(1 — X₁).
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