Solution Found!
Let Y1 < Y2 < · · · < Yn be the order statistics of a
Chapter 6, Problem 9E(choose chapter or problem)
QUESTION:
Let \(Y_1 < Y_2 < \cdots < Y_n\) be the order statistics of a random sample of size n from an exponential distribution with pdf \(f(x) = e^{-x}, 0 < x < \infty\).
(a) Find the pdf of \(Y_r\).
(b) Determine the pdf of \(U = e^{−Y_r}\).
Questions & Answers
QUESTION:
Let \(Y_1 < Y_2 < \cdots < Y_n\) be the order statistics of a random sample of size n from an exponential distribution with pdf \(f(x) = e^{-x}, 0 < x < \infty\).
(a) Find the pdf of \(Y_r\).
(b) Determine the pdf of \(U = e^{−Y_r}\).
ANSWER:Step 1 of 3
Given:
is the order statistics of a random sample of size n from an exponential distribution.
The probability density function is given as,