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Correlated random variables

  1. Jan 11, 2008 #1
    I have two independent standard normal random variables X1,X2. Now I want to construct two new normal random variables Y1,Y2 with mean[tex]\mu[/tex]1, [tex]\mu[/tex]2 and variance ([tex]\sigma[/tex]1)^2, ([tex]\sigma[/tex]2)^2 and correlation [tex]\rho[/tex].
    How do I approach this problem?
     
  2. jcsd
  3. Jan 12, 2008 #2

    mathman

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    Y1=s1X1+m1
    Y2=bX1+cX2+m2
    where b2+c2=s22
    b=rs2, therefore c=s2(1-r2)1/2
     
  4. Jan 13, 2008 #3
    Thanks mathman.
    But what was your thought process? How did you come up with these relations?
     
  5. Jan 13, 2008 #4

    mathman

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    From long past experience I know that to get correlated normal variables from uncorrrelated standard normal, you just need a linear combination. Adding the desired means is obvious. Also since there are four free coefficients and there are only three conditions, I just set one coefficient to 0.
     
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