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Let X₁, X₂,..., X be an independent identical random sample from a population with a Rayleigh distribution with the density function : X -X f(x 0) = exp ; x > 0 82 20² 1. show that the probability function is an exponential family

Let X₁, X₂,..., X be an independent identical random sample from a population with a Rayleigh distribution with the density function : X -X f(x 0) = exp ; x > 0 82 20² 1. show that the probability function is an exponential family

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.CR: Chapter 13 Review
Problem 29CR
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Let X₁, X₂, ..., Xn be an independent identical random sample from a population with a Rayleigh distribution with the density function : x -X² f(x0) = oz exp ; x > 0 82 20² 1. show that the probability function is an exponential family 2. define fairly complete statistics for 3. if the strongest test is carried out to test Ho: 0 = 0,5 against H₁ 8 = 2 in your opinion, is the hypothesis a simple or composite hypothesis? tell f (X1,.. ...,Xn0o) ****** 4. find 2 (x₁,...,xn|0o; 0₁ ₁) = - f (x₁. .Xn01) 5. determine the test rejection area
Transcribed Image Text:Let X₁, X₂, ..., Xn be an independent identical random sample from a population with a Rayleigh distribution with the density function : x -X² f(x0) = oz exp ; x > 0 82 20² 1. show that the probability function is an exponential family 2. define fairly complete statistics for 3. if the strongest test is carried out to test Ho: 0 = 0,5 against H₁ 8 = 2 in your opinion, is the hypothesis a simple or composite hypothesis? tell f (X1,.. ...,Xn0o) ****** 4. find 2 (x₁,...,xn|0o; 0₁ ₁) = - f (x₁. .Xn01) 5. determine the test rejection area
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