Explanation Given: The quartile points for a probability density function are the values x 1 , x 2 , x 3 that divide the area under the graph of the function into four equal parts. Definition used: Cumulative distribution functions : If f is a probability function and F ( x ) = ∫ − ∞ x f ( t ) d t is the associated cumulative distribution function. Calculation: The given function is f ( x ) = { 1 ( 1 + x ) 2 if x ≥ 0 0 othewise . If x < 0 , then F ( x ) = 0 . In case of x ≥ 0 , the value of F ( x ) is as follows. F ( x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ 0 0 d t + ∫ 0 x 1 ( 1 + t ) 2 d t = ( − 1 ( 1 + t ) ) 0 x = − 1 ( 1 + x ) − − 1 ( 1 + 0 ) On further simplification, F ( x ) = − 1 ( 1 + x ) + 1 = − 1 + 1 + x ( 1 + x ) = x ( 1 + x ) Thus, the value of F ( x ) is F ( x ) = { 0 , x < 0 x 1 + x , x ≥ 0

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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Chapter 11.3, Problem 40E

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To find: The quartile points for the probability density function f(x)={1(1+x)2 if x≥00 othewise.

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Chapter 11.3, Problem 39E

Chapter 11.3, Problem 41E

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Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The quartile points for the probability density function f ( x ) = { 1 ( 1 + x ) 2 if x ≥ 0 0 othewise .

Solution Summary: The author calculates the quartile points for the probability density function f(x)=l

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To find: The quartile points for the probability density function f(x)={1(1+x)2 if x≥00 othewise.

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Chapter 11 Solutions