For constants o > 0 and a > 0, the function aoª p(x) xa+1> where x > 0, is called a Pareto distribution. It is often used in modeling the distribution of incomes or wealth in a population. In the income interpretation, the function P(x) = p(t)dt,
For constants o > 0 and a > 0, the function aoª p(x) xa+1> where x > 0, is called a Pareto distribution. It is often used in modeling the distribution of incomes or wealth in a population. In the income interpretation, the function P(x) = p(t)dt,
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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(d) Suppose = 10, 000 and = 1.2. Find A, P(A), and P(2A). Interpret the
meaning of these values.
Transcribed Image Text:8. For constants o > 0 and a > 0, the function
ασα
p(x) :
xa+1’
where x > o, is called a Pareto distribution. It is often used in modeling the distribution
of incomes or wealth in a population. In the income interpretation, the function
P(æ) = | p(t)dt,
x > 0, gives the proportion of the population whose income exceeds x. Here o repre-
sents the minimum income of any person in the population and a controls how rapidly
the income distribution diminishes as x increases.
(a) Find P(x).
(b) If a > 1, the average income of a population described by this model is
A =
xp(x)dx.
Find A.
(c) Why is the condition a > 1 needed in (b)?
(d) Suppose o
meaning of these values.
10, 000 and a
1.2. Find A, P(A), and P(2A). Interpret the
(e) Find the general expression for P(A) as a function of a and graph it. Use this
graph to interpret the fairness of the income distribution for different values of a.
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