Homework Help is Here – Start Your Trial Now!
Math
Statistics
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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
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.)
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.)
Expert Solution
Description

We need to find the likelihood function of the given distributions.

Exp(λ), Geometric(p), Poisson(λ), and N(μ,σ2).

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS