(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.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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part C D

3. Let X = {X1, X2, . . . , Xn} be a random sample from the probability distribution
with probability density function:
(202 /x for c > 0
f (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)% confidence
interval for 0.
Transcribed Image Text:3. Let X = {X1, X2, . . . , Xn} be a random sample from the probability distribution with probability density function: (202 /x for c > 0 f (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)% confidence interval for 0.
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