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Math Help - Joint distribution

  1. #1
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    Joint distribution

    The joint distribution of X and Y is given by f(x,y)= (exp(-y)/y)
    0<x<y<infinity
    I need to compute E(X^2 + Y^2 | Y=y)

    can anyone please guide me on how to do this.

    Thank You very much for Your help
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  2. #2
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    Using  f(x|y) = f(x,y) f(y), you can calculate the integral

     \iint \left(x^2 + y^2 \right) f(x|y)dxdy

    And to find  f(y) you have to calculate the integral

     \int_o^y f(x,y)dx
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  3. #3
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    Quote Originally Posted by gustavodecastro View Post
    Using  f(x|y) = f(x,y) f(y),

    Why is this?
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  4. #4
    MHF Contributor matheagle's Avatar
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    E(X^2 + Y^2 | Y=y)= E(X^2|Y=y) + y^2

    and E(X^2|Y=y)=\int x^2 f(x|y)dx
    Last edited by matheagle; September 3rd 2009 at 05:10 PM.
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  5. #5
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    is f(y) then =exp(-y) or Ei(-y)?
    and if f(y) is equal to exp(-y)
    is then
    E(X^2+Y^2|Y0Y)
    equal to [(exp(-2y)x^3)/3y]+[y^2] ?

    really appreciate the help
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  6. #6
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    Quote Originally Posted by gustavodecastro View Post
    Using  f(x|y) = f(x,y) f(y), you can calculate the integral

     \iint \left(x^2 + y^2 \right) f(x|y)dxdy

    And to find  f(y) you have to calculate the integral

     \int_o^y f(x,y)dx
    is it dy or dx in the end of the integral defining f(y)?
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  7. #7
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    dx

    and

    f(x|y) = \frac{f(x,y)}{f(y)}
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