The distributions of incomes in two cities follow the two

Chapter 5, Problem 7E

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QUESTION:

The distributions of incomes in two cities follow the two Pareto-type pdfs

\(f(x)=\frac{2}{x^{3}}, \quad 1<x<\infty$, and $g(y)=\frac{3}{y^{4}}, \quad 1<y<\infty\),

respectively. Here one unit represents $20,000. One person with income is selected at random from each city. Let \(X\) and \(Y\) be their respective incomes. Compute \(P(X < Y)\).

Equation Transcription:


 

 

Text Transcription:

f(x)=2/x^3, 1<x<infinity

g(y)=3/y^4, 1<y<infinity  

X  

Y  

P(X<Y)

Questions & Answers

QUESTION:

The distributions of incomes in two cities follow the two Pareto-type pdfs

\(f(x)=\frac{2}{x^{3}}, \quad 1<x<\infty$, and $g(y)=\frac{3}{y^{4}}, \quad 1<y<\infty\),

respectively. Here one unit represents $20,000. One person with income is selected at random from each city. Let \(X\) and \(Y\) be their respective incomes. Compute \(P(X < Y)\).

Equation Transcription:


 

 

Text Transcription:

f(x)=2/x^3, 1<x<infinity

g(y)=3/y^4, 1<y<infinity  

X  

Y  

P(X<Y)

ANSWER:

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