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Math Help - Pareto type PDFs

  1. #1
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    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).
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  2. #2
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    Quote Originally Posted by wolverine21 View Post
    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:

    \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.
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  3. #3
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    How would you tackle this problem using the cdf technique. I am struggling on how to set up the limits of integration.

    Thanks!
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