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a) b) c) where k> 0 is a constant. Show that the maximum likelihood estimator (MLE) of the parameter 1 is  = XXX Show with reasons whether or not  is unbiased for 2. Find the mean square error of 1.

a) b) c) where k> 0 is a constant. Show that the maximum likelihood estimator (MLE) of the parameter 1 is  = XXX Show with reasons whether or not  is unbiased for 2. Find the mean square error of 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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Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: a) b) c) d) e) f) f(x; 2) = λ-kxk-1e (k-1)! 0, if x > 0, elsewhere where k> 0 is a constant. X Show that the maximum likelihood estimator (MLE) of the parameter 1 is λ = Show with reasons whether or not î is unbiased for 1. Find the mean square error of 1. Find the Fisher information inequality of the parameter 1. Justify whether or not â is a uniform minimum variance unbiased estimator of 1. Check whether or not the MLE of λ is a consistent. Suggest with a Fisher's factorization theorem, the sufficient estimator of 1.
Transcribed Image Text:Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: a) b) c) d) e) f) f(x; 2) = λ-kxk-1e (k-1)! 0, if x > 0, elsewhere where k> 0 is a constant. X Show that the maximum likelihood estimator (MLE) of the parameter 1 is λ = Show with reasons whether or not î is unbiased for 1. Find the mean square error of 1. Find the Fisher information inequality of the parameter 1. Justify whether or not â is a uniform minimum variance unbiased estimator of 1. Check whether or not the MLE of λ is a consistent. Suggest with a Fisher's factorization theorem, the sufficient estimator of 1.
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