Explanation Given information: E ( X ) = B − ∫ A B F ( x ) d x . Formula used: 1) Let X be a continuous random variable whose possible values lie between A and B , and f ( x ) be the probability density function for X . Then, the expected value (average) of X is the number E ( X ) defined by, E ( X ) = ∫ A B x f ( x ) d x . 2) Integration by parts ∫ f ( x ) ⋅ g ( x ) d x = F ( x ) g ( x ) − ∫ F ( x ) ⋅ g ' ( x ) d x Proof: Consider, F ( x ) is an anti-derivative of f ( x ) and if g ( x ) = x ⇒ g ' ( x ) = 1 . By definition of the expected value, E ( X ) = ∫ A B x f ( x ) d x

Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version

14th Edition

ISBN: 9780134463230

Author: Larry J. Goldstein, David I Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 12.3, Problem 25E

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To prove: E(X) = B − ∫ABF(x) dx, where F(x) is the cumulative distribution function for X on A ≤ x ≤ B.

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Chapter 12.3, Problem 24E

Chapter 12.3, Problem 26E

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Chapter 12 Solutions

Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version

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Ch. 12.1 - Decision Making Based on Expected Value A citrus...Ch. 12.1 - Prob. 10E Ch. 12.2 - Prob. 1CYU Ch. 12.2 - Prob. 2CYU Ch. 12.2 - Prob. 1E Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Prob. 10E Ch. 12.2 - Prob. 11E Ch. 12.2 - Prob. 12E Ch. 12.2 - Prob. 13E Ch. 12.2 - Prob. 14E Ch. 12.2 - Prob. 15E Ch. 12.2 - Prob. 16E Ch. 12.2 - Prob. 17E Ch. 12.2 - Prob. 18E Ch. 12.2 - Prob. 19E Ch. 12.2 - Prob. 20E Ch. 12.2 - Prob. 21E Ch. 12.2 - Prob. 22E Ch. 12.2 - Prob. 23E Ch. 12.2 - Prob. 24E Ch. 12.2 - Prob. 25E Ch. 12.2 - Prob. 26E Ch. 12.2 - An experiment consists of selecting a point at...Ch. 12.2 - Prob. 28E Ch. 12.2 - Prob. 29E Ch. 12.2 - Prob. 30E Ch. 12.2 - Prob. 31E Ch. 12.2 - Prob. 32E Ch. 12.2 - Prob. 33E Ch. 12.2 - Prob. 34E Ch. 12.2 - Prob. 35E Ch. 12.2 - A random variable X has a cumulative distribution...Ch. 12.2 - Prob. 37E Ch. 12.2 - Prob. 38E Ch. 12.3 - 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To prove: E ( X ) = B − ∫ A B F ( x ) d x , where F ( x ) is the cumulative distribution function for X on A ≤ x ≤ B .

Solution Summary: The author explains the formula used to prove that E(X) is an anti-derivative of f(x).

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To prove: E(X) = B − ∫ABF(x) dx, where F(x) is the cumulative distribution function for X on A ≤ x ≤ B.

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Chapter 12 Solutions