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(Stat 467 only) Let X₁,..., Xn be a random sample from standard uniform distribution. (a) Determine the cumulative distribution function (CDF) and the probability density function (PDF) of the first order statistic X (1) (the minimum of the sample). Make sure to properly account for the domains.

(Stat 467 only) Let X₁,..., Xn be a random sample from standard uniform distribution. (a) Determine the cumulative distribution function (CDF) and the probability density function (PDF) of the first order statistic X (1) (the minimum of the sample). Make sure to properly account for the domains.

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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6. (Stat 467 only) Let X₁,..., Xn be a random sample from standard uniform distribution. (a) Determine the cumulative distribution function (CDF) and the probability density function (PDF) of the first order statistic X(1) (the minimum of the sample). Make sure to properly account for the domains. (b) Determine the cumulative distribution function (CDF) and the probability density function (PDF) of the largest order statistic X(n) (the maximum of the sample). Make sure to properly account for the domains. (c) Graph the PDFs of X₁, X(1), and X(n) and write a short paragraph explaining how the three distributions are different.
Transcribed Image Text:6. (Stat 467 only) Let X₁,..., Xn be a random sample from standard uniform distribution. (a) Determine the cumulative distribution function (CDF) and the probability density function (PDF) of the first order statistic X(1) (the minimum of the sample). Make sure to properly account for the domains. (b) Determine the cumulative distribution function (CDF) and the probability density function (PDF) of the largest order statistic X(n) (the maximum of the sample). Make sure to properly account for the domains. (c) Graph the PDFs of X₁, X(1), and X(n) and write a short paragraph explaining how the three distributions are different.
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