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Math Help - Simple Covariance Theory

  1. #1
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    Simple Covariance Theory

    In this problem, there is a given f(x) (continuous case)
    and they say that U=X and v=X
    the first question is
    a)find that Cov(U,V) = 0 which is easily done
    then,
    b)show that U and V are DEPENDANT.

    Now I know that if U and V and independant, Cov(U,V) = 0
    although the converse is not true.
    But now, how do I show that U and V are dependant?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by suissa View Post
    In this problem, there is a given f(x) (continuous case)
    and they say that U=X and v=X
    the first question is
    a)find that Cov(U,V) = 0 which is easily done
    then,
    b)show that U and V are DEPENDANT.

    Now I know that if U and V and independant, Cov(U,V) = 0
    although the converse is not true.
    But now, how do I show that U and V are dependant?
    p(u,v)=q(u)r(v)

    RonL
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  3. #3
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    But what is q and what is r?
    and i assume p(u,v) means probability of u and v?

    Thanks.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by suissa View Post
    But what is q and what is r?
    and i assume p(u,v) means probability of u and v?

    Thanks.
    They are the densities of the marginal distributions of u and v.

    RonL
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  5. #5
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    Ahhhh
    You use marginals to show it!
    Smart.
    Thanks a lot.
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