Explanation Given Information: The provided function is, f ( x ) = { c x 3 x ≥ 100 0 otherwise Formula used: If f ( x ) ≥ 0 for all x , then for a continuous random variable x , f is a probability density function if and only if, ∫ − ∞ ∞ f ( x ) d x = 1 If the limit defining the improper integral is a unique finite number, then integral converges else it diverges, ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x According to the power rule of integrals, ∫ x n d x = x n + 1 n + 1 + C Calculation: Consider the provided function, f ( x ) = { c x 3 x ≥ 100 0 otherwise Now, if ∫ − ∞ 100 0 d x + ∫ 100 ∞ c x − 3 d x = 1 then the function will be probability density function. Use the formula, ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x To rewrite the integral as, ∫ − ∞ ∞ f ( x ) d x = ∫ − ∞ 100 0 d x + ∫ 100 ∞ c x − 3 d x </

WebAssign Printed Access Card for Harshbarger/Reynolds' Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition, Multi-Term

12th Edition

ISBN: 9781337630542

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Question

Chapter 13.7, Problem 30E

To determine

To calculate: The value of c in the function f(x)={cx3x≥1000otherwise so that this function is a probability density function.

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Chapter 13.7, Problem 29E

Chapter 13.7, Problem 31E

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Chapter 13 Solutions

WebAssign Printed Access Card for Harshbarger/Reynolds' Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition, Multi-Term

Ch. 13.1 - CHECKPOINT 1. For the interval [0, 2]. determine...Ch. 13.1 - Prob. 2CP Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E

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The value of c in the function f ( x ) = { c x 3 x ≥ 100 0 otherwise so that this function is a probability density function.

Solution Summary: The author calculates that the value of c in the function is a probability density function.

To calculate: The value of c in the function f(x)={cx3x≥1000otherwise so that this function is a probability density function.

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Chapter 13 Solutions