# Correlated random variables

1. Jan 11, 2008

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?

2. Jan 12, 2008

### mathman

Y1=s1X1+m1
Y2=bX1+cX2+m2
where b2+c2=s22
b=rs2, therefore c=s2(1-r2)1/2

3. Jan 13, 2008

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

4. Jan 13, 2008

### mathman

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.