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Suppose you have a random sample of n observations from a distribution with pdf Ge-(x-c)/0 for x >c 1. given by f (x) = }° can be shown that E(X) = 0 + c and Var(X) = 6². Show that the method of moments estimator of 0 is X – c, where X is the sample mean. where c is a nonnegative constant and 0 is positive. It otherwise' a. b. Show that the maximum likelihood estimator of 0 is also X- c. You do not have to check the second derivative to ensure it is a maximum.

Suppose you have a random sample of n observations from a distribution with pdf Ge-(x-c)/0 for x >c 1. given by f (x) = }° can be shown that E(X) = 0 + c and Var(X) = 6². Show that the method of moments estimator of 0 is X – c, where X is the sample mean. where c is a nonnegative constant and 0 is positive. It otherwise' a. b. Show that the maximum likelihood estimator of 0 is also X- c. You do not have to check the second derivative to ensure it is a maximum.

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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Nhat is the MSE of the estimator ô = X – c? (Hint: This will be an expression in terms of e and n.)
Transcribed Image Text:Nhat is the MSE of the estimator ô = X – c? (Hint: This will be an expression in terms of e and n.)
1. Suppose you have a random sample of n observations from a distribution with pdf Ge-(x-c)/0 for x > c where c is a nonnegative constant and 0 is positive. It given by f (x) = otherwise can be shown that E (X) = 0 + c and Var(X) = 02. Show that the method of moments estimator of e is X – c, where X is the sample mean. a. b. . Show that the maximum likelihood estimator of 0 is also X – c. You do not have to check the second derivative to ensure it is a maximum.
Transcribed Image Text:1. Suppose you have a random sample of n observations from a distribution with pdf Ge-(x-c)/0 for x > c where c is a nonnegative constant and 0 is positive. It given by f (x) = otherwise can be shown that E (X) = 0 + c and Var(X) = 02. Show that the method of moments estimator of e is X – c, where X is the sample mean. a. b. . Show that the maximum likelihood estimator of 0 is also X – c. You do not have to check the second derivative to ensure it is a maximum.
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