Correlated random variables

  • Thread starter gradnu
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  • #1
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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?
 

Answers and Replies

  • #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
 
  • #3
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Thanks mathman.
But what was your thought process? How did you come up with these relations?
 
  • #4
mathman
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Thanks mathman.
But what was your thought process? How did you come up with these relations?

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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