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: 9781319050733

Author: Rogawski

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Chapter 9.1, Problem 10E

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

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Chapter 9.1, Problem 9E

Chapter 9.1, Problem 11E

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To prove: The density function p ( x ) = 2 π ( x 2 + 1 ) on [ 0 , ∞ ) 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 9 Solutions