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Expectation of a Joint Continuous rv

  1. Apr 19, 2009 #1
    fx,y = 6(x-y)dydx, if 0<y<x<1

    how do you find E(XY),
    i know the formula...g(x,y)fxy(x,y)dydx

    but i dont know what 'g(x,y)' represents and the limits to use??
  2. jcsd
  3. Apr 19, 2009 #2

    matt grime

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    The expectation of g(X,Y) is

    [tex]\mathbb{E}(g(X,Y)):= \int g(x,y)f(x,y)\mathrm{d}x\mathrm{d}y[/tex]

    with the integral being taken over the whole of the probability space of X and Y.

    So here, g(X,Y) is XY, and the limits are given to you: 0<y<x<1.
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