## correlated random variables

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

Recognitions:
Science Advisor

## correlated random variables

 Quote by gradnu 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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