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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 8, both > 0, and the pdf is as follows. k.gk x 28 f(x; k, 0)=k+1 0 х<0 (a) Sketch the graph of f(x; k, 0). f(x) f(x) f(x) f(x) k 8 0 (b) Verify that the total area under the graph equals 1. for kiek d . dx = xk+1 (c) If the rv X has pdf f(x; k, e), for any fixed b>0, obtain an expression for P(X ≤ b). (d) For 8 < a

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 8, both > 0, and the pdf is as follows. k.gk x 28 f(x; k, 0)=k+1 0 х<0 (a) Sketch the graph of f(x; k, 0). f(x) f(x) f(x) f(x) k 8 0 (b) Verify that the total area under the graph equals 1. for kiek d . dx = xk+1 (c) If the rv X has pdf f(x; k, e), for any fixed b>0, obtain an expression for P(X ≤ b). (d) For 8 < a

Algebra & Trigonometry with Analytic Geometry
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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Part B and 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. k.ak f(x; k, 0) = ΧΣΘ xx +1 0 x < 0 (a) Sketch the graph of f(x; k, 0). f(x) f(x) f(x) f(x) SLED k 0 k A (b) Verify that the total area under the graph equals 1. 6. k.gk xk+1 dx = = 0-8 off (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).
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. k.ak f(x; k, 0) = ΧΣΘ xx +1 0 x < 0 (a) Sketch the graph of f(x; k, 0). f(x) f(x) f(x) f(x) SLED k 0 k A (b) Verify that the total area under the graph equals 1. 6. k.gk xk+1 dx = = 0-8 off (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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