Answered: A random variable is called a power law…

A random variable is called a power law random variable ifP(X > t) = max{1/(t^α), 1}for some α. What is the density of X? Compute the mean of X when α > 1. What happens if α < 1?

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

Section13.3: Special Probability Density Functions

Problem 30E

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A random variable is called a power law random variable if
P(X > t) = max{1/(t^α), 1}
for some α. What is the density of X? Compute the mean of X when α > 1. What happens if α < 1?

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