Explanation Given information: f ( x ) = k x 2 , 0 ≤ x ≤ 2 . 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 by 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 2 , 0 ≤ x ≤ 2 Therefore ∫ a b f ( x ) d x = 1 </

15th Edition

ISBN: 9780137590438

Author: Goldstein

Publisher: PEARSON

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Question

Chapter 12.2, Problem 8E

To determine

To calculate: The value of k , such that the function f(x)=kx2, 0≤x≤2 is a probability density function on the specified interval.

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Chapter 12.2, Problem 7E

Chapter 12.2, Problem 9E

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Chapter 12 Solutions

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Knowledge Booster

The value of k , such that the function f ( x ) = k x 2 , 0 ≤ x ≤ 2 is a probability density function on the specified interval.

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

To calculate: The value of k , such that the function f(x)=kx2, 0≤x≤2 is a probability density function on the specified interval.

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Chapter 12 Solutions