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Suppose that X;:i = 1,2, 3, . n are independent random variables with a common uni form distribution over (0, 1) and Y, is distributed over (0, Y-1) with Yo = 1,k = 1,2, ., n. Let 2, = []x.. k = 1,2,3, .n R.D.R EGALA STAT 203 March 4, 2021 Show by mathematical induction induction or any other method that Z, has probability density function (-In z)*-1 fa(z) = (k – 1)! k = 1,2,3, . n Hence deduce that Zg and Yg have the same distribution (k = 1,2,3,.n)

Suppose that X;:i = 1,2, 3, . n are independent random variables with a common uni form distribution over (0, 1) and Y, is distributed over (0, Y-1) with Yo = 1,k = 1,2, ., n. Let 2, = []x.. k = 1,2,3, .n R.D.R EGALA STAT 203 March 4, 2021 Show by mathematical induction induction or any other method that Z, has probability density function (-In z)*-1 fa(z) = (k – 1)! k = 1,2,3, . n Hence deduce that Zg and Yg have the same distribution (k = 1,2,3,.n)

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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Suppose that X;; i = 1,2, 3, .. n are independent random variables with a common uniform distribution over (0, 1) and Yg is distributed over (0, Yg -1) with Y, =1,k = 1,2, ..., n. Let Z = k = 1,2,3, .n R.D.R EGALA STAT 203 March 4, 2021 Show by mathematical induction induction or any other method that Zg has probability density function (-In z)*-1 fR(z) = k = 1,2,3, . n (k – 1)! Hence deduce that Zg and Y, have the same distribution (k = 1,2,3, ..n)
Transcribed Image Text:Suppose that X;; i = 1,2, 3, .. n are independent random variables with a common uniform distribution over (0, 1) and Yg is distributed over (0, Yg -1) with Y, =1,k = 1,2, ..., n. Let Z = k = 1,2,3, .n R.D.R EGALA STAT 203 March 4, 2021 Show by mathematical induction induction or any other method that Zg has probability density function (-In z)*-1 fR(z) = k = 1,2,3, . n (k – 1)! Hence deduce that Zg and Y, have the same distribution (k = 1,2,3, ..n)
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