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Math Help - Formulas for dependent RV's

  1. #1
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    Formulas for dependent RV's

    X and Y are random variables with standard deviation \sigma_X=0.2 and \sigma_Y=0.2. They are both distributed normally, with \mu_X=\mu_Y=0 and correlation \rho_{XY}=-0.2 (they are not independent).

    (a) Find the standard deviations of 3X.

    Is this just 3(0.2) = 0.6?

    (b) Find the standard deviation of X - Y

    How do I do this is X and Y are not independent? What is the formula for dependent RVs?

    (C) What is P(|X-Y|>1)?

    Thank you.
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  2. #2
    MHF Contributor matheagle's Avatar
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    (a) is fine

    (b)  V(X-Y)=V(X)+V(Y)-2Cov(X,Y).

    Where the correlation equals  {Cov(X,Y)\over \sigma_x\sigma_y}.

    So, Cov(X,Y)=(.2)(.2)(-.2).

    (c) Here you need to standardize X-Y, by subtracting off its mean, which clearly is 0 and dividing by it's standard deviation.
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