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Math Help - The Covariance of Two Random Variables

  1. #1
    Junior Member atalay's Avatar
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    The Covariance of Two Random Variables

    It is known that when random variables X and Y independent, cov(X,Y)=0. However, inverse is not true. Show that, by an example, that we can have cov(X,Y)=0 and X and Y are not independent.
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    Super Member Anonymous1's Avatar
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    Quote Originally Posted by atalay View Post
    It is known that when random variables X and Y independent, cov(X,Y)=0. However, inverse is not true. Show that, by an example, that we can have cov(X,Y)=0 and X and Y are not independent.
    Here is one...

    X takes values \{-1,0,1\} with probabilities \{\frac{1}{3}, \frac{1}{3}, \frac{1}{3}\}.

    Let Y = X^2.

    Cov(X,Y) = EX^3 - EXEX^2 = 0

    Since, EX = EX^3 = 0.

    But clearly X and Y are dependent.
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    Junior Member atalay's Avatar
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    thanks but i do not understand some symbols, etc. frac. Sorry about this.
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    Super Member Anonymous1's Avatar
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    Quote Originally Posted by atalay View Post
    thanks but i do not understand some symbols, etc. frac. Sorry about this.
    I was working out the LaTex. See above.
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  5. #5
    Junior Member atalay's Avatar
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    ok. the problem is solved. thanks.
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