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1) 1) Use part d) of question 2 to show that is a consistent estimator of 8. Show that In(X) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family]. Estimate 8 using the method of moment estimator.

1) 1) Use part d) of question 2 to show that is a consistent estimator of 8. Show that In(X) is a sufficient estimator of 0. [Hint: Use one-parameter regular exponential family]. Estimate 8 using the method of moment estimator.

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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Please answer f and g

Let X₁, X2, X3,..., X₁ denote a random sample of size n from the population distributed with the following probability density function: a) b) d) e) f) g) f(x;0) = {(0+¹)xº, if 0<x< 1 elsewhere What is the parameter space of 0? Find the maximum likelihood estimator (MLE) of 8. What is the MLE of g(0) ==? Suppose that is a uniform minimum variance unbiased estimator of 8. Show that the variance of ê, Var(8) = (0+1)² n Use part d) of question 2 to show that is a consistent estimator of 0. Show that In (X;) is a sufficient estimator of 9. [Hint: Use one-parameter regular exponential family]. Estimate using the method of moment estimator.
Transcribed Image Text:Let X₁, X2, X3,..., X₁ denote a random sample of size n from the population distributed with the following probability density function: a) b) d) e) f) g) f(x;0) = {(0+¹)xº, if 0<x< 1 elsewhere What is the parameter space of 0? Find the maximum likelihood estimator (MLE) of 8. What is the MLE of g(0) ==? Suppose that is a uniform minimum variance unbiased estimator of 8. Show that the variance of ê, Var(8) = (0+1)² n Use part d) of question 2 to show that is a consistent estimator of 0. Show that In (X;) is a sufficient estimator of 9. [Hint: Use one-parameter regular exponential family]. Estimate using the method of moment estimator.
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