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Let X, , X, be a random sample from a Normal distribution with mean u and variance a. Given that the maximum likelihood estimator (MLE) of µ is a = &. find the MLE of o? and comment on your answer. You may use L = L(H, a²) = (2no²)-n/zexp

Let X, , X, be a random sample from a Normal distribution with mean u and variance a. Given that the maximum likelihood estimator (MLE) of µ is a = &. find the MLE of o? and comment on your answer. You may use L = L(H, a²) = (2no²)-n/zexp

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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a) Let X,,X, be a random sample from a Normal distribution with mean u and variance a. Given that the maximum likelihood estimator (MLE) of u is A = X. find the MLE of g? and comment on your answer. £(x¡ – µ)ª] You may use L = L(H, o?) = (2no?)-n/2exp b) Show that X is a sufficient estimator of the mean u of a Normal population with known variance o? based on a random sample X,,X use L(6; x) = g(y: 6)h(x,,xm), where y = u(x1,***, Xn). c) Let X, .,X, denote a random sample from a distribution with p.d.f f(x; 8) = e-(x-#); x > 6 Use the method of moments to estimate the parameter 0. d) Let X4, ...,X, denote a random sample from a distribution with p.d.f. (Ine)* f(x) ={ ex;! 0, x 2 0 and 0 >1 elsewhere Determine the MLE for Ine. II
Transcribed Image Text:a) Let X,,X, be a random sample from a Normal distribution with mean u and variance a. Given that the maximum likelihood estimator (MLE) of u is A = X. find the MLE of g? and comment on your answer. £(x¡ – µ)ª] You may use L = L(H, o?) = (2no?)-n/2exp b) Show that X is a sufficient estimator of the mean u of a Normal population with known variance o? based on a random sample X,,X use L(6; x) = g(y: 6)h(x,,xm), where y = u(x1,***, Xn). c) Let X, .,X, denote a random sample from a distribution with p.d.f f(x; 8) = e-(x-#); x > 6 Use the method of moments to estimate the parameter 0. d) Let X4, ...,X, denote a random sample from a distribution with p.d.f. (Ine)* f(x) ={ ex;! 0, x 2 0 and 0 >1 elsewhere Determine the MLE for Ine. II
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