Let X₁, X₂, ..., X, be an independent identical random sample from a population with a Rayleigh distribution with the density function : 2 x -X f(x10) = 7/2² exp ; x > 0 82 20² 1. show that the probability function is an exponential family 2. define fairly complete statistics for 0 3. if the strongest test is carried out to test Ho: 0 = 0,5 against H₁: 0 = 2 in your opinion, is the hypothesis a simple or composite hypothesis? tell 4. find 2 (x₁,...,xn|0o; 0₁ ) = f (X1Xn|0o) Xn01) f (x₁.. 5. determine the test rejection area
Let X₁, X₂, ..., X, be an independent identical random sample from a population with a Rayleigh distribution with the density function : 2 x -X f(x10) = 7/2² exp ; x > 0 82 20² 1. show that the probability function is an exponential family 2. define fairly complete statistics for 0 3. if the strongest test is carried out to test Ho: 0 = 0,5 against H₁: 0 = 2 in your opinion, is the hypothesis a simple or composite hypothesis? tell 4. find 2 (x₁,...,xn|0o; 0₁ ) = f (X1Xn|0o) Xn01) f (x₁.. 5. determine the test rejection area
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please answer number 4
![Let X₁, X₂, ..., X, 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf1fe36c-8059-4dcd-9777-e6dd77e5596a%2Fe9505bb8-44db-4b50-8c37-6395b5088a7f%2Fbgzg7vc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X₁, X₂, ..., X, 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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