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1) Let X₁, X₂,..., X, be random sample of size n that distributed according to exponential distribution with mean a) Explain why Y() is not a pivotal quantity? (Note that Y() is the maximum order statistic). nY (1) b) Explain why Q= is a pivotal quantity? (Note that Y) is the 1st order 0 statistic). c) Based on the pivotal quantity, derive the 90% confidence interval for 0. (Identify values of a and b in the confidence interval).

1) Let X₁, X₂,..., X, be random sample of size n that distributed according to exponential distribution with mean a) Explain why Y() is not a pivotal quantity? (Note that Y() is the maximum order statistic). nY (1) b) Explain why Q= is a pivotal quantity? (Note that Y) is the 1st order 0 statistic). c) Based on the pivotal quantity, derive the 90% confidence interval for 0. (Identify values of a and b in the confidence interval).

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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1) Let X₁, X₂,..., X, be random sample of size n that distributed according to exponential distribution with mean a) Explain why Y() is not a pivotal quantity? (Note that Y() is the maximum order statistic). nY (1) b) Explain why Q= is a pivotal quantity? (Note that Y) is the 1st order 0 statistic). c) Based on the pivotal quantity, derive the 90% confidence interval for 0. (Identify values of a and b in the confidence interval).
Transcribed Image Text:1) Let X₁, X₂,..., X, be random sample of size n that distributed according to exponential distribution with mean a) Explain why Y() is not a pivotal quantity? (Note that Y() is the maximum order statistic). nY (1) b) Explain why Q= is a pivotal quantity? (Note that Y) is the 1st order 0 statistic). c) Based on the pivotal quantity, derive the 90% confidence interval for 0. (Identify values of a and b in the confidence interval).
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