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9. Let p(x) = 4 T(1 + (2x)²) for 20 (and p(a) = 0 if a <0). (a) Show that p is a probability density function. (b) If X is the associated random variable, find the median of X. (c) Show that the mean of X is infinite. This is strange: A finite amount of "mass" can be distributed along the positive number line in a way such that the line does not balance at any point, but instead tips infinitely hard to the right at each location.

9. Let p(x) = 4 T(1 + (2x)²) for 20 (and p(a) = 0 if a <0). (a) Show that p is a probability density function. (b) If X is the associated random variable, find the median of X. (c) Show that the mean of X is infinite. This is strange: A finite amount of "mass" can be distributed along the positive number line in a way such that the line does not balance at any point, but instead tips infinitely hard to the right at each location.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 29CR
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9. Let p(x) = 4 T(1 + (2x)²) for 20 (and p(a) = 0 if a <0). (a) Show that p is a probability density function. (b) If X is the associated random variable, find the median of X. (c) Show that the mean of X is infinite. This is strange: A finite amount of "mass" can be distributed along the positive number line in a way such that the line does not balance at any point, but instead tips infinitely hard to the right at each location.
Transcribed Image Text:9. Let p(x) = 4 T(1 + (2x)²) for 20 (and p(a) = 0 if a <0). (a) Show that p is a probability density function. (b) If X is the associated random variable, find the median of X. (c) Show that the mean of X is infinite. This is strange: A finite amount of "mass" can be distributed along the positive number line in a way such that the line does not balance at any point, but instead tips infinitely hard to the right at each location.
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