A family of pdf's that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. The family has two parameters, k and 0, both > 0, and the pdf is as follows. k. gk x20 f(x; k, 0) = + 1 (a) Sketch the graph of f(x; k, 0). f(x) f(x) f(x) f(x) k (b) Verify that the total area under the graph equals 1. dx= (c) If the rv X has pdf f(x; k, 0), for any fixed b > 0, obtain an expression for P(X s b). (d) For 0 < a < b, obtain an expression for the probability P(a sxs b).
A family of pdf's that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. The family has two parameters, k and 0, both > 0, and the pdf is as follows. k. gk x20 f(x; k, 0) = + 1 (a) Sketch the graph of f(x; k, 0). f(x) f(x) f(x) f(x) k (b) Verify that the total area under the graph equals 1. dx= (c) If the rv X has pdf f(x; k, 0), for any fixed b > 0, obtain an expression for P(X s b). (d) For 0 < a < b, obtain an expression for the probability P(a sxs b).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Need help with b,c,d
![A family of pdf's that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. The family has two parameters, k and 0, both > 0, and the pdf is as follows.
gk
f(x; k, ө) 3D
x < 0
(a) Sketch the graph of f(x; k, 0).
f(x)
f(x)
f(x)
f(x)
X
X
X
k
k
(b) Verify that the total area under the graph equals 1.
ok
dx =
+ 1
]:
Je x*
= 0 -
ok
=|1
(c) If the rv X has pdf f(x; k, 0), for any fixed b > 0, obtain an expression for P(X < b).
(d) For 0 < a < b, obtain an expression for the probability P(a < X < b).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7e43dbe-ab72-46fa-955b-a8f42ce6613a%2F98b2ca5f-7c81-4c21-a45e-cb39c0cbaecc%2Fzz5gkl4_processed.png&w=3840&q=75)
Transcribed Image Text:A family of pdf's that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. The family has two parameters, k and 0, both > 0, and the pdf is as follows.
gk
f(x; k, ө) 3D
x < 0
(a) Sketch the graph of f(x; k, 0).
f(x)
f(x)
f(x)
f(x)
X
X
X
k
k
(b) Verify that the total area under the graph equals 1.
ok
dx =
+ 1
]:
Je x*
= 0 -
ok
=|1
(c) If the rv X has pdf f(x; k, 0), for any fixed b > 0, obtain an expression for P(X < b).
(d) For 0 < a < b, obtain an expression for the probability P(a < X < b).
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