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Math Help - 2 dependent random variables with Covariance = 0

  1. #1
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    2 dependent random variables with Covariance = 0

    I'm new to proofing and advanced maths, so I need help with this task:

    --
    given two random variables X & Y, where:

    Y = -X if -c <= X <= c
    Y = X if X is not in the interval [-c,c]

    show that c can be chosen so that Cov(X,Y) = 0, but that the two random variables are dependent.
    --

    I can see the variables are clearly dependent, but I find it really hard to find the c value. Can anyone help?
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  2. #2
    MHF Contributor matheagle's Avatar
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    Let's see, you want E(XY)=E(X)E(Y) where Y=X\left(1-2I(|X|\le c)\right)
    Last edited by matheagle; October 29th 2010 at 11:10 PM.
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