Let X₁, X₂, ..., X, be an independent identical random samp with a Rayleigh distribution with the density func population

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Please answer number 2
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
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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