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?

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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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?

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Follow-up Question

How to find MME using the Pdf give above?

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.

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