(iii) Show that 1/7 is also a sufficient statistic for each of these three distributions.
(iii) Show that 1/7 is also a sufficient statistic for each of these three distributions.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
part iii (i already asked part i and part ii)
![In lecture (Mon 1/30), we showed that
• for Bernoulli (p) distribution, the MLE estimator
p=ī
Exercise 1
is sufficient for the parameter p;
for Uniform([a, b]), the MLE estimators
Geometric (p)
Poisson(X)
are jointly sufficient for the parameters a, b.
In this exercise, you will deduce similar results for the following four distributions:
• Exp(x)
• N(μ1,0²)
â = y₁ = min(x₁, · · , £n), b = Yn :=: max(F₁,..., In)
(i) For each of these four distributions, write down their likelihood functions. (Hint: the
log-likelihood functions for these distributions were computed in previous lecture and
homework.)
(ii) Use the Fisher-Neyman factorization theorem to show that is a sufficient statistic
for each of the first three distributions.
(iii) Show that 1/7 is also a sufficient statistic for each of these three distributions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04625ac1-43ff-4999-b93a-55388fc0c5e2%2Fdc64e850-ef9e-4cbf-bc72-c4e6a0184c85%2F4ek5pgf_processed.png&w=3840&q=75)
Transcribed Image Text:In lecture (Mon 1/30), we showed that
• for Bernoulli (p) distribution, the MLE estimator
p=ī
Exercise 1
is sufficient for the parameter p;
for Uniform([a, b]), the MLE estimators
Geometric (p)
Poisson(X)
are jointly sufficient for the parameters a, b.
In this exercise, you will deduce similar results for the following four distributions:
• Exp(x)
• N(μ1,0²)
â = y₁ = min(x₁, · · , £n), b = Yn :=: max(F₁,..., In)
(i) For each of these four distributions, write down their likelihood functions. (Hint: the
log-likelihood functions for these distributions were computed in previous lecture and
homework.)
(ii) Use the Fisher-Neyman factorization theorem to show that is a sufficient statistic
for each of the first three distributions.
(iii) Show that 1/7 is also a sufficient statistic for each of these three distributions.
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