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Math Help - [SOLVED] Expected value of f(x,y) - Simple question

  1. #1
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    Red face [SOLVED] Expected value of f(x,y) - Simple question

    Ok, I know this is rather simple, but I need to refresh my memory on this:

    f(x,y) = xy 0<x<y<1

    I want to find E(x).

    I know I should do E(x) = integral(1 to x), integral(0,y) [x*(xy)]dxdy.

    However, I also know I've probably screwed up on the integration limits. Can somebody double check on this. My final answer should be a # right? Thanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by spearfish View Post
    Ok, I know this is rather simple, but I need to refresh my memory on this:

    f(x,y) = xy 0<x<y<1

    I want to find E(x).

    I know I should do E(x) = integral(1 to x), integral(0,y) [x*(xy)]dxdy.

    However, I also know I've probably screwed up on the integration limits. Can somebody double check on this. My final answer should be a # right? Thanks
    Note that 0<x<y<1. x<y<1 tells us that we are considering values above the line y=x and below the line y=1. Also, we can conclude from restriction given that x goes from 0 to 1.

    Therefore, the integral should be \int_0^1\int_x^1 x^2y\,dy\,dx.

    Does this make sense?
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  3. #3
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    yeah, I can see what you're saying. I ll watch out for this next time.
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  4. #4
    MHF Contributor matheagle's Avatar
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    I'd integrate the x first, that way both lower bounds of integration are zero.
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