3. The Pareto distribution is a common probability distribution for describing quantities that follow so-called power laws (e.g., maximum one-day rainfall totals in different locations, the sizes of files transmitted via the Internet, etc.). Here we will use calculus again to learn a bit more about this distribution. a) Suppose you were given the cdf for this distribution: x < Xmin 0, F(x) (Xmin` ,х > Хmin х Differentiate the cdf with respect to x to obtain the pdf. [You can check your answer by looking on Wikipedia.] b) Assuming that a > 1, show that the mean/expected value of this distribution is given by: αχmin E(X) : a – 1
3. The Pareto distribution is a common probability distribution for describing quantities that follow so-called power laws (e.g., maximum one-day rainfall totals in different locations, the sizes of files transmitted via the Internet, etc.). Here we will use calculus again to learn a bit more about this distribution. a) Suppose you were given the cdf for this distribution: x < Xmin 0, F(x) (Xmin` ,х > Хmin х Differentiate the cdf with respect to x to obtain the pdf. [You can check your answer by looking on Wikipedia.] b) Assuming that a > 1, show that the mean/expected value of this distribution is given by: αχmin E(X) : a – 1
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![3. The Pareto distribution is a common probability distribution for describing quantities that
follow so-called power laws (e.g., maximum one-day rainfall totals in different locations, the
sizes of files transmitted via the Internet, etc.). Here we will use calculus again to learn a bit
more about this distribution.
a) Suppose you were given the cdf for this distribution:
x < Xmin
0,
F(x)
(Xmin`
,х > Хmin
х
Differentiate the cdf with respect to x to obtain the pdf. [You can check your answer by
looking on Wikipedia.]
b) Assuming that a > 1, show that the mean/expected value of this distribution is given by:
αχmin
E(X) :
a – 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b13e23e-77c2-4463-be56-996e1bb2f2c9%2Fa3029aa9-3327-4808-883a-8248f4f75ff4%2F7iiy7dr.png&w=3840&q=75)
Transcribed Image Text:3. The Pareto distribution is a common probability distribution for describing quantities that
follow so-called power laws (e.g., maximum one-day rainfall totals in different locations, the
sizes of files transmitted via the Internet, etc.). Here we will use calculus again to learn a bit
more about this distribution.
a) Suppose you were given the cdf for this distribution:
x < Xmin
0,
F(x)
(Xmin`
,х > Хmin
х
Differentiate the cdf with respect to x to obtain the pdf. [You can check your answer by
looking on Wikipedia.]
b) Assuming that a > 1, show that the mean/expected value of this distribution is given by:
αχmin
E(X) :
a – 1
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