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Math Help - Correlation coefficient

  1. #1
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    Correlation coefficient

    i have another qns here

    if the correlation coefficient between X and Y is ρxy=1

    how to prove that σ(X+Y) = σX + σY ?
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  2. #2
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    Hello,

    By definition, 1=\rho_{XY}=\frac{cov(X,Y)}{\sigma_X\sigma_Y} \Rightarrow cov(X,Y)=\sigma_X\sigma_Y (1)

    But we know that \sigma^2(X+Y)=\sigma^2_X+\sigma^2_Y+2 cov(X,Y) (2)

    Just replace (1) in (2) and you're done.
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  3. #3
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    ok! i got it! thanks!! =D
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