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  1. #1
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    expectations

    Given that (X,Y) have pdf f(x,y)=2 and x+y=1. How do i find E(X+Y).

    how doi decide the range tt i should integrate from since it cant be from infinity to neg ininty ?
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    Given that (X,Y) have pdf f(x,y)=2 and x+y=1. How do i find E(X+Y).

    how doi decide the range tt i should integrate from since it cant be from infinity to neg ininty ?
    I doubt that you have posted the whole question exactly as it was originally stated.

    eg. The question probably said that the support was the region bounded by x \geq 0, y \geq 0 and x + y \leq 1. In which case, you set up the appropriate double integral of f(x, y) over that region.

    Have you been taught double integration at all?
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  3. #3
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    yes i was taught how to use double integral. iwas thinking tt i need to findE(X) andE(Y) seperatedly.in tt case, wewont need to usedouble integral right?
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    Quote Originally Posted by alexandrabel90 View Post
    yes i was taught how to use double integral. iwas thinking tt i need to findE(X) andE(Y) seperatedly.in tt case, wewont need to usedouble integral right?
    You would then need the marginals.

    My advice:

    Calculate \int \int_{R_{xy}} (x + y) f(x, y) \, dx \, dy where R_{xy} is region of integration.

    (And you still have not said whether you posted the complete question or not).
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  5. #5
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    sorry i missed tht part of the question. i just checked and the region that u said is the correct region that the question is asking for. sorryfor that mstake.
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  6. #6
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    the complete question is let (X,Y) have bivariate pdf f(x,y)=2 and bounded by x+y=1 in the first quadrant. find E(X+Y).
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  7. #7
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    may i know what is the region of integration?

    initially what i did was integrate from 0 to (1-y) for xf(x,y)dx + integrate from 0 to (1-x) yf(x,y)dy ...i was trying to use marginals..but i wasnt sure what is the range that i should integrate from...

    from my working above, the range that i have integrated is obviously wrong..

    if i were to use your method, would the range be form 0 to (1-y) dx and then 0 to 1 dy?

    thanks!
    Last edited by alexandrabel90; March 21st 2010 at 04:13 AM.
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  8. #8
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    Quote Originally Posted by alexandrabel90 View Post
    may i know what is the region of integration?

    initially what i did was integrate from 0 to (1-y) for xf(x,y)dx + integrate from 0 to (1-x) yf(x,y)dy ...i was trying to use marginals..but i wasnt sure what is the range that i should integrate from...

    from my working above, the range that i have integrated is obviously wrong..

    if i were to use your method, would the range be form 0 to (1-y) dx and then 0 to 1 dy?

    thanks!
    Yes.
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