Let Y1 < Y2 < Y3 < Y4 < Y5 be the order statistics of five

Chapter 6, Problem 3E

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QUESTION:

Let \(Y_{1}<Y_{2}<Y_{3}<Y_{4}<Y_{5}\) be the order statistics of five independent observations from an exponential distribution that has a mean of \(\theta=3\).

(a) Find the pdf of the sample median \(Y_{3}\).

(b) Compute the probability that \(Y_{4}\) is less than 5.

(c) Determine \(P\left(1<Y_{1}\right)\).

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QUESTION:

Let \(Y_{1}<Y_{2}<Y_{3}<Y_{4}<Y_{5}\) be the order statistics of five independent observations from an exponential distribution that has a mean of \(\theta=3\).

(a) Find the pdf of the sample median \(Y_{3}\).

(b) Compute the probability that \(Y_{4}\) is less than 5.

(c) Determine \(P\left(1<Y_{1}\right)\).

ANSWER:

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\(Y_{1}<Y_{2}<Y_{3}<Y_{4}<Y_{5}\)  is the order statistics of five independent observations from an exponential distribution that has a mean of \(\theta=3\).

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