Explanation Given information: p ( x ) = 2 π ( x 2 + 1 ) Formula used: The mean value is μ = ∫ − ∞ ∞ x . p ( x ) d x Proof: p ( x ) = 2 π ( x 2 + 1 ) (Given) Its mean value is given by μ = ∫ − ∞ ∞ x . p ( x ) d x = ∫ 0 ∞ x . 2 π ( x 2 + 1 ) d x = 1 π ∫ 0 ∞ 2 x ( x 2 + 1 ) d x Let u = x 2 +

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ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 8.8, Problem 8E

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To prove: The density function p(x)=2π(x2+1) on [0,∞) has infinite mean.

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Chapter 8.8, Problem 7E

Chapter 8.8, Problem 9E

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Chapter 8 Solutions

Calculus - Standalone book

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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To prove: The density function p ( x ) = 2 π ( x 2 + 1 ) on [ 0 , ∞ ) has infinite mean.

Solution Summary: The author explains how the density function p(x)=2pi (x 2+1) has infinite mean.

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To prove: The density function p(x)=2π(x2+1) on [0,∞) has infinite mean.

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Chapter 8 Solutions