4. Probability maximization: We have independent random variables X and Y with distribution X ~ Poisson (p) and Y~ Poisson (20), and observations x = 2 and y = 5 of these. (a) Show that the expression for the log-likelihood function is given by: l(φ) = [5 ln (2) - - In (2!) - ln (5!)] + 7 ln ¢ − 30. - Plot 1() for values of € [0,10] (a rough sketch is OK). For what value of does l() have its maximum? (b) Calculate the probability maximization estimator for the observed values x = 2 and y = 5.
4. Probability maximization: We have independent random variables X and Y with distribution X ~ Poisson (p) and Y~ Poisson (20), and observations x = 2 and y = 5 of these. (a) Show that the expression for the log-likelihood function is given by: l(φ) = [5 ln (2) - - In (2!) - ln (5!)] + 7 ln ¢ − 30. - Plot 1() for values of € [0,10] (a rough sketch is OK). For what value of does l() have its maximum? (b) Calculate the probability maximization estimator for the observed values x = 2 and y = 5.
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
4b)
![4. Probability maximization: We have independent random variables X and Y with distribution X~
Poisson (p) and Y~ Poisson (20), and observations x = 2 and y = 5 of these.
(a) Show that the expression for the log-likelihood function is given by:
ι(φ)
[5 ln (2) In (2!)
In (5!)] + 7 ln p – 30.
Plot 1() for values of € [0,10] (a rough sketch is OK). For what value of p does l() have its
maximum?
(b) Calculate the probability maximization estimator for the observed values x = 2 and y = 5.
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78f3f25b-2eb2-4186-b342-f9f487e8326d%2Fb158f207-4d82-4270-beea-b009dee83da2%2F03o40ck_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Probability maximization: We have independent random variables X and Y with distribution X~
Poisson (p) and Y~ Poisson (20), and observations x = 2 and y = 5 of these.
(a) Show that the expression for the log-likelihood function is given by:
ι(φ)
[5 ln (2) In (2!)
In (5!)] + 7 ln p – 30.
Plot 1() for values of € [0,10] (a rough sketch is OK). For what value of p does l() have its
maximum?
(b) Calculate the probability maximization estimator for the observed values x = 2 and y = 5.
=
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