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Thread: Correlation

  1. #1
    Senior Member chella182's Avatar
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    Jan 2008
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    Correlation

    $\displaystyle X$ and $\displaystyle Y$ are random variables with expectation equal to zero and variances $\displaystyle \sigma^2$ and $\displaystyle \omega^2\sigma^2$ respectively.
    a) If $\displaystyle X$ and $\displaystyle Y$ are independent show that the correlation of $\displaystyle X+Y$ and $\displaystyle X-Y$ is

    $\displaystyle \frac{1-\omega^2}{1+\omega^2}$.

    b) Find the corresponding correlation if $\displaystyle X$ and $\displaystyle Y$ are not independent but have correlation $\displaystyle \rho$.
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  2. #2
    Newbie
    Joined
    Apr 2010
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    how about starting with the defintion of correlation in terms of covariance?
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