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Math Help - conditional expected value of bivariate normal

  1. #1
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    conditional expected value of bivariate normal

    Let X~N(1,1), Y~N(2,1) be bivariate normal with cov(X,Y)=1/2. Obtain E(Y|X).

    I see that you can get E(XY) using the covariance, but I don't see where that leads. The only way I know to calculate the conditional expectation is by integrating over the density function of Y given X, which is so ugly in this case that there's certainly an easier approach.
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  2. #2
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    Quote Originally Posted by Beaky View Post
    Let X~N(1,1), Y~N(2,1) be bivariate normal with cov(X,Y)=1/2. Obtain E(Y|X).

    I see that you can get E(XY) using the covariance, but I don't see where that leads. The only way I know to calculate the conditional expectation is by integrating over the density function of Y given X, which is so ugly in this case that there's certainly an easier approach.
    Do you already know that E(Y|X)=aX+b for some a,b? (this is a general fact with Gaussian vectors) If so, then you can find a,b from the values of E[Y] and E[XY] (they lead to a system of equations).
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