
#1
Jan1108, 05:13 PM

P: 21

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
Jan1208, 11:28 PM

Sci Advisor
P: 5,939

Y_{1}=s_{1}X_{1}+m_{1}
Y_{2}=bX_{1}+cX_{2}+m_{2} where b^{2}+c^{2}=s_{2}^{2} b=rs_{2}, therefore c=s_{2}(1r^{2})^{1/2} 



#3
Jan1308, 11:27 AM

P: 21

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



#4
Jan1308, 05:56 PM

Sci Advisor
P: 5,939

correlated random variables 


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