MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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(d) Suppose  = 10, 000 and  = 1.2. Find A, P(A), and P(2A). Interpret the

meaning of these values.

 

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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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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