Explanation Given information: The median of an exponential distribution is the number M such that Pr ( X ≤ M ) = 1 2 . Formula used: The cumulative distribution function: Pr ( X ≤ b ) = ∫ 0 b k e − k x d x . Exponential rule of integration : ∫ e a x d x = e a x a + C Proof: By using the cumulative distribution function, Pr ( X ≤ M ) = ∫ 0 M k e − k x d x Substitute Pr ( X ≤ M ) = 1 2 in the above function. 1 2 = ∫ 0 M k e − k x d x ⇒ 1 2 = k ∫ 0 M e − k x d <

12th Edition

ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

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Chapter 12.4, Problem 34E

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To prove: That M=(ln2)/k, where the median of an exponential density function is that number M such that Pr (X≤M)=12.

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Chapter 12.4, Problem 33E

Chapter 12.4, Problem 35E

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To prove: That M = ( ln 2 ) / k , where the median of an exponential density function is that number M such that Pr ( X ≤ M ) = 1 2 .

Solution Summary: The author explains that the median of an exponential density function is that number M such that mathrmPr(Xle M)=12

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To prove: That M=(ln2)/k, where the median of an exponential density function is that number M such that Pr (X≤M)=12.

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Chapter 12 Solutions