In this exercise, you will deduce similar results for the following four distributions: Exp(X) Geometric (p) • Poisson(X) • N(μ1,0²) (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
In this exercise, you will deduce similar results for the following four distributions: Exp(X) Geometric (p) • Poisson(X) • N(μ1,0²) (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
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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![Exercise 1
In lecture (Mon 1/30), we showed that
• for Bernoulli (p) distribution, the MLE estimator
p=x
is sufficient for the parameter p;
for Uniform([a, b]), the MLE estimators
Geometric (p)
â = y₁ = min(x₁,...,xn), b = yn := max(x₁,-, Tn)
are jointly sufficient for the parameters a, b.
In this exercise, you will deduce similar results for the following four distributions:
• Exp(x)
• Poisson(X)
•N(1,0²)
(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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04625ac1-43ff-4999-b93a-55388fc0c5e2%2Fb4d26962-3260-4358-ab41-fb4d41ad4e76%2Fupo8d2o_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 1
In lecture (Mon 1/30), we showed that
• for Bernoulli (p) distribution, the MLE estimator
p=x
is sufficient for the parameter p;
for Uniform([a, b]), the MLE estimators
Geometric (p)
â = y₁ = min(x₁,...,xn), b = yn := max(x₁,-, Tn)
are jointly sufficient for the parameters a, b.
In this exercise, you will deduce similar results for the following four distributions:
• Exp(x)
• Poisson(X)
•N(1,0²)
(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.)
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