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Math Help - Expectation Question

  1. #1
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    Expectation Question

    if we know

    E[X|a <= x<=b]=0
    E[Y|c <= y<=d]=0
    Z=X-Y

    Do we know if

    E[Z|-a-d<=z<=b-c]=0?

    Thanks a lot for help.
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  2. #2
    Member
    Joined
    May 2006
    Posts
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    Quote Originally Posted by gracelhz View Post
    if we know

    E[X|a <= x<=b]=0
    E[Y|c <= y<=d]=0
    Z=X-Y

    Do we know if

    E[Z|-a-d<=z<=b-c]=0?

    Thanks a lot for help.
    No because:

    let a=c=0, b=d=1

    and:

    p(0 <= x<=1)=0 and p(c <= y<=d)=0

    and:

    p(x=7)=1, p(y=6.5)=1.

    (and probability of any other result be 0)

    Then E[Z|-1<=z<=1]=0.5

    .
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