Explanation Given: The function is f ( x ) = 3 2 x 2 − 3 x . Concept used: The probability lies in the interval [ a , b ] can be expressed as below. P ( a ≤ X ≤ b ) = ∫ a b f ( x ) d x ...... ( 1 ) Here, the probability P ( a ≤ X ≤ b ) lies between 0 and 1. Here, f ( x ) is the probability density function that is non-negative on the interval [ a , b ] . Calculation: The function is shown below. f ( x ) = 3 2 x 2 − 3 x The probability on the interval [ 1 , 3 ] can be calculated as follows: P ( 1 ≤ X ≤ 3 ) = ∫ 1 3 ( 3 2 x 2 − 3 x ) d x = 3 2 ( x 3 3 ) 1 3 − 3 ( x 2 2 ) 1 3 = 3 2 ( 1 3 ) ( 3 3 − 1 3</

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Question

Chapter 10.1, Problem 66E

To determine

Whether the statement “The function f(x)=32x2−3x is a probability density function on [1,3]” is true or false.

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Chapter 10.1, Problem 65E

Chapter 10.1, Problem 1TE

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Chapter 10 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 10.1 - Define the following terms in your own words: a....Ch. 10.1 - Prob. 2CQ Ch. 10.1 - Prob. 3CQ Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E

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Knowledge Booster

Whether the statement “The function f ( x ) = 3 2 x 2 − 3 x is a probability density function on [ 1 , 3 ] ” is true or false.

Solution Summary: The author analyzes whether the statement "The function f(x)=32x

Whether the statement “The function f(x)=32x2−3x is a probability density function on [1,3]” is true or false.

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Chapter 10 Solutions