Let Y1 < Y2 < · · · < Yn be the order statistics of a

Chapter 6, Problem 9E

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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 \(U = e^{−Y_r}\).

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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,

                                                                   

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