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Math Help - Bivariate normal Distribution

  1. #1
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    Bivariate normal Distribution

    Show that for standard bivariate normal variables X and Y with correlation "rho"

    E(max(X,Y)) = sqrt((1-rho)/pi)

    Thanks in advance
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  2. #2
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    Quote Originally Posted by realfunboy View Post
    Show that for standard bivariate normal variables X and Y with correlation "rho"

    E(max(X,Y)) = sqrt((1-rho)/pi)

    Thanks in advance
    Several approaches are possible.

    One approach might start by first proving that the two random variables X and U = \frac{Y - \rho X}{\sqrt{1 - \rho^2}} are independent and standard normal. Then note that Y > X if and only if (1 - \rho) X < \sqrt{1 - \rho^2} U.
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