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Let Y1 < Y2 < Y3 < Y4 < Y5 be the order statistics of five
Chapter 6, Problem 3E(choose chapter or problem)
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 \(P\left(1<Y_{1}\right)\).
Questions & Answers
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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:Step 1 of 4
Given:
\(Y_{1}<Y_{2}<Y_{3}<Y_{4}<Y_{5}\) is the order statistics of five independent observations from an exponential distribution that has a mean of \(\theta=3\).
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