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Question about covariance

  1. May 13, 2013 #1
    Let X1 and Y1 be two random variables. We have Cov(X1,Y1) = 0. Does this extend to any transformation X2 = g(X1) and Y2 = g(Y1), such that Cov(X2,Y2)? Here, g is a continuous function. For example, if we set X2 = X1^2 and Y2 = Y1^2. Do we then from Cov(X1,Y1) = 0 that Cov(X1^2,Y1^2) = 0?
     
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  3. May 13, 2013 #2

    D H

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    No. For example, if X1 and Y1 are uncorrelated but not independent, then your X2 and Y2 may have a non-zero correlation.
     
  4. May 13, 2013 #3

    Stephen Tashi

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    For example, try random variables X and Y with the joint distribution given by:

    P(X=-2,Y=3) = 1/4
    P(X=-1,Y=2) = 1/4
    P(X=1,Y=2) = 1/4
    P(X=2,Y=3) = 1/4

    and transform by g(w) = w^2
     
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