Explanation Given information: A probability density function is given by p ( x ) = 2 π ( x 2 + 1 ) on the interval [ 0 , ∞ ) . Formula used: For a probability density function p ( x ) on ( − ∞ , ∞ ) , the mean μ of the random variable is given by μ = ∫ − ∞ ∞ x p ( x ) d x The integral below can be calculated as. ∫ x x 2 + 1 d x = 1 2 ln | x 2 + 1 | + C Calculation: Let us consider the given probability density function. p ( x ) = 2 π ( x 2 + 1 ) Now calculate the mean of the probability density function on [ 0 , ∞ ) as shown below

4th Edition

ISBN: 9781319308858

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 8.1, Problem 10E

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

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Chapter 8.1, Problem 9E

Chapter 8.1, Problem 11E

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

Solution Summary: The author explains the probability density function p(x)=2pi (x

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

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Chapter 8 Solutions

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

Solution Summary: The author explains the probability density function p(x)=2pi (x

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

Want to see the full answer?

Chapter 8 Solutions

To show:

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