2) Let X₁, X₂, X3, X4 be a random sample of size 4 from a population with the following distribution function f(x: 0)=B e (x-4) for x > 4 otherwise Where, ß > 0. a) If f(x; 0) a member of one-parameter regular exponential family. What are the functions h(x), c(0), w (0) and t(x). b) Find the maximum likelihood estimator of the parameter B. c) If the data from this random sample are 8.2,9.1, 10.6 and 4.9, respectively, what is the maximum likelihood estimate of B?
2) Let X₁, X₂, X3, X4 be a random sample of size 4 from a population with the following distribution function f(x: 0)=B e (x-4) for x > 4 otherwise Where, ß > 0. a) If f(x; 0) a member of one-parameter regular exponential family. What are the functions h(x), c(0), w (0) and t(x). b) Find the maximum likelihood estimator of the parameter B. c) If the data from this random sample are 8.2,9.1, 10.6 and 4.9, respectively, what is the maximum likelihood estimate of B?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 25EQ
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Question
![2) Let X₁, X2, X3, X4 be a random sample of size 4 from a population with the following
distribution function
1
f(x; 0)=B
= {
(x-4)
e B for x > 4
otherwise
Where, ß > 0.
a) If f(x; 0) a member of one-parameter regular exponential family. What are the
functions h(x), c(0), w(0) and t(x).
b) Find the maximum likelihood estimator of the parameter ß.
c)
If the data from this random sample are 8.2, 9.1, 10.6 and 4.9, respectively, what
is the maximum likelihood estimate of ß?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5725e27e-e3a8-4329-aa13-e0519d950c8c%2F2042a408-e6dd-4667-a41e-dd9cabf323b3%2Fr7lavl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2) Let X₁, X2, X3, X4 be a random sample of size 4 from a population with the following
distribution function
1
f(x; 0)=B
= {
(x-4)
e B for x > 4
otherwise
Where, ß > 0.
a) If f(x; 0) a member of one-parameter regular exponential family. What are the
functions h(x), c(0), w(0) and t(x).
b) Find the maximum likelihood estimator of the parameter ß.
c)
If the data from this random sample are 8.2, 9.1, 10.6 and 4.9, respectively, what
is the maximum likelihood estimate of ß?
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Follow-up Questions
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Follow-up Question
How to find MME using the
![2) Let X₁, X₂, X3, X4 be a random sample of size 4 from a population with the following
distribution function
Where, ß > 0.
1
-е
f(x; 0) = B
0,
(x-4)
B
ilo
for x > 4
otherwise
m
Lumapam
e) Repeat a) and b) using the method of moments.](https://content.bartleby.com/qna-images/question/45e373be-e798-432d-b765-67c0741e74af/e57a79f8-7707-4dbb-a6bc-3b31da36c192/xp805w9_thumbnail.jpeg)
Transcribed Image Text:2) Let X₁, X₂, X3, X4 be a random sample of size 4 from a population with the following
distribution function
Where, ß > 0.
1
-е
f(x; 0) = B
0,
(x-4)
B
ilo
for x > 4
otherwise
m
Lumapam
e) Repeat a) and b) using the method of moments.
Solution
Follow-up Question
![2) Let X₁, X₂, X3, X4 be a random sample of size 4 from a population with the following
distribution function
Where, ß > 0.
1
-е
f(x; 0) = B
0,
(x-4)
B
ilo
for x > 4
otherwise
m
Lapan
e) Repeat a) and b) using the method of moments.](https://content.bartleby.com/qna-images/question/45e373be-e798-432d-b765-67c0741e74af/332091e8-5a71-4b4c-a98b-18bcf1af92dc/jcxj2w4_thumbnail.jpeg)
Transcribed Image Text:2) Let X₁, X₂, X3, X4 be a random sample of size 4 from a population with the following
distribution function
Where, ß > 0.
1
-е
f(x; 0) = B
0,
(x-4)
B
ilo
for x > 4
otherwise
m
Lapan
e) Repeat a) and b) using the method of moments.
Solution
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