Thread: Pareto type PDFs

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

f(x) = 2/x^3 1 < x < infinity and g(y) = 3/y^4 1 <y < infinity

Here one unit represents 20,000 dollars. One person with income is selected at random from city and let X and Y be their respective incomes.

Compute P(X < Y)

how do you compute that probability. I'm not sure how to approach P(X<Y).

Originally Posted by wolverine21

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

f(x) = 2/x^3 1 < x < infinity and g(y) = 3/y^4 1 <y < infinity

Here one unit represents 20,000 dollars. One person with income is selected at random from city and let X and Y be their respective incomes.

Compute P(X < Y)

how do you compute that probability. I'm not sure how to approach P(X<Y).

Are X and Y independent? If so then:

$\displaystyle \Pr(X < Y) = \int_{x = 1}^{+\infty} \int_{y = x}^{+\infty} f(x) \cdot g(y) \, dy \, dx$.

Draw the region in the xy plane to see where the integral terminals have come from.

Reed-

How would you tackle this problem using the cdf technique. I am struggling on how to set up the limits of integration.

Thanks!