Question 1: Let X₁,..., X, be a sample from the probability distribution with density = S 07° x-(0+1) if x > Y Pe,(x)= { 0 else, where > 0 and > 0 are parameters. Assume that y = 1 and 0 is unknown for (a), (b) and (c) . (a) Show that the maximum likelihood estimator for is given by n Σlog Xi (b) Construct an exact 95% confidence interval for 0. (c) Construct an asymptotic 95% confidence interval for 0.
Question 1: Let X₁,..., X, be a sample from the probability distribution with density = S 07° x-(0+1) if x > Y Pe,(x)= { 0 else, where > 0 and > 0 are parameters. Assume that y = 1 and 0 is unknown for (a), (b) and (c) . (a) Show that the maximum likelihood estimator for is given by n Σlog Xi (b) Construct an exact 95% confidence interval for 0. (c) Construct an asymptotic 95% confidence interval 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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Transcribed Image Text:Question 1: Let X₁,..., X, be a sample from the probability distribution with density
=
S 07° x-(0+1) if x > Y
Pe,(x)=
{
0
else,
where > 0 and > 0 are parameters.
Assume that y = 1 and 0 is unknown for (a), (b) and (c) .
(a) Show that the maximum likelihood estimator for is given by
n
Σlog Xi
(b) Construct an exact 95% confidence interval for 0.
(c) Construct an asymptotic 95% confidence interval for 0.
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