Explanation Given information: f ( x ) = k / x , 1 ≤ x ≤ 4 . Formula used: Power rule of integration ∫ x n d x = x n + 1 n + 1 , n ≠ − 1 Calculation: A probability density function is a function f defined an interval ( a , b ) and having the following properties. i) f ( x ) ≥ 0 for every x . ii) ∫ a b f ( x ) d x = 1 Probability density function f ( x ) = k / x , 1 ≤ x ≤ 4 Therefore, ∫ a b f ( x ) d x = 1 ⇒ ∫ 1 4 k / x d x = 1 Take the constant k outside the integral, ⇒ k ∫ 1 4 1 / x d x = 1 ⇒ k

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 12.2, Problem 10E

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To calculate: The value of k, such that the function f(x)=k/x, 1≤x≤4 is a probability density function on the specified interval.

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Chapter 12.2, Problem 9E

Chapter 12.2, Problem 11E

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The value of k , such that the function f ( x ) = k / x , 1 ≤ x ≤ 4 is a probability density function on the specified interval.

Solution Summary: The author explains that a probability density function is defined an interval (a,b,) and having the following properties.

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To calculate: The value of k, such that the function f(x)=k/x, 1≤x≤4 is a probability density function on the specified interval.

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Chapter 12 Solutions