# correlated random variables

Tags: correlated, random, variables
 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$$\mu$$1, $$\mu$$2 and variance ($$\sigma$$1)^2, ($$\sigma$$2)^2 and correlation $$\rho$$. How do I approach this problem?
 Sci Advisor P: 5,768 Y1=s1X1+m1 Y2=bX1+cX2+m2 where b2+c2=s22 b=rs2, therefore c=s2(1-r2)1/2
 P: 21 Thanks mathman. But what was your thought process? How did you come up with these relations?