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(a) Verify that f(y|0) belongs to an exponential family in traditional form. (b) Determine the likelihood function L(0) for this random sample. (c) Show that the maximum likelihood estimator of 0 is 1/3 ÔMLE = i=1

(a) Verify that f(y|0) belongs to an exponential family in traditional form. (b) Determine the likelihood function L(0) for this random sample. (c) Show that the maximum likelihood estimator of 0 is 1/3 ÔMLE = i=1

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
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f (y|0) 3y? exp 03 03 provided y > 0 where 0 > 0 is a parameter. Note that if Y ~ f(y|0), then E(Y³) = 0³. = 0³. (a) Verify that f(y|0) belongs to an exponential family in traditional form. (b) Determine the likelihood function L(0) for this random sample. (c) Show that the maximum likelihood estimator of 0 is 1/3 ÔMLE 3 n i=1 You may use any method that we discussed in class for finding the MLE. (d) Find the Fisher information I(0) in a single observation from this density. (e) Using the standard normal approximation for the distribution of a maximum likelihood estimator based on the Fisher information, construct an approximate 95% confidence interval for 0. Note that z0.025 1.96.
Transcribed Image Text:f (y|0) 3y? exp 03 03 provided y > 0 where 0 > 0 is a parameter. Note that if Y ~ f(y|0), then E(Y³) = 0³. = 0³. (a) Verify that f(y|0) belongs to an exponential family in traditional form. (b) Determine the likelihood function L(0) for this random sample. (c) Show that the maximum likelihood estimator of 0 is 1/3 ÔMLE 3 n i=1 You may use any method that we discussed in class for finding the MLE. (d) Find the Fisher information I(0) in a single observation from this density. (e) Using the standard normal approximation for the distribution of a maximum likelihood estimator based on the Fisher information, construct an approximate 95% confidence interval for 0. Note that z0.025 1.96.
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