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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: d) e) f) g) f(x; 0) = {(0+1)xº, if 0

Let X₁, X2, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: d) e) f) g) f(x; 0) = {(0+1)xº, if 0

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: d) e) f) g) f(x; 0) = {(0+1)xº, if 0<x<1 elsewhere Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance (0+1)² of ê, Var(8)=5 n Use part d) of question 2 to show that is a consistent estimator of 0. Show that In (X₁) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family]. Estimate using the method of moment estimator.
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: d) e) f) g) f(x; 0) = {(0+1)xº, if 0<x<1 elsewhere Suppose that is a uniform minimum variance unbiased estimator of 0. Show that the variance (0+1)² of ê, Var(8)=5 n Use part d) of question 2 to show that is a consistent estimator of 0. Show that In (X₁) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family]. Estimate using the method of moment estimator.
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