3. Let X = {X1, X2, . . . , Xn} be a random sample from the probability distributionwith probability density function:(202 /x for c > 0f (x; 0) =0.otherwise.(a) Find a sufficient statistic for 0.(b) Find the maximum likelihood estimator of 0.(c) Find a pivotal function of the maximum likelihood estimator found in (b).(d) Use the pivotal function obtained in (c) to construct a 100(1– a)% confidenceinterval for 0.

Answered: Image /qna-images/answer/93d97733-a949-4868-8b47-be13169b0112.jpg

Answered: (a) Find a sufficient statistic for 0.…

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) Find a sufficient statistic for 0. (b) Find the maximum likelihood estimator of 0. (c) Find a pivotal function of the maximum likelihood estimator found in (b). (d) Use the pivotal function obtained in (c) to construct a 100(1- a)% confidence interval for 0.