# Math Help - Correlation of Two Random Variables

1. ## Correlation of Two Random Variables

If X and Y have a bivariate normal distribution function with parameters μx, μy, σx̄, σy, ρ. Let U=X+Y and V=X-Y. Find an expression for correlation coefficient of U and V.

I did this question but i am not sure because i am confused for U and V. How do this problem?

2. $Cov(X-Y,X+Y) =V(X)+Cov(X,Y)-Cov(X,Y)-V(Y) =V(X)-V(Y)$

$V(X-Y) =V(X)-2Cov(X,Y)+V(Y)$

$V(X+Y) =V(X)+2Cov(X,Y)+V(Y)$

So $V(X+Y)V(X-Y) =\left(V(X)+V(Y)\right)^2-4\left(Cov(X,Y)\right)^2$

3. Thanks, i did.

i found that

μu=μx+μy and μv=μx-μy σu=σv=σx^2+σy^2+2ρσxσx

Corr(X,Y)= ρ, so Cov (X,Y)= ρσxσy

Cov(U,V)=Cov(X,X)+(-1)Cov(X,Y)+Cov(Y,X)+(-1)Cov(Y,Y)=Var (X)-Var(Y)

Corr(U,V)=Cov(U,V)/σuσv=σx^2-σy^2/σuσv

4. this part is incorrect

Originally Posted by atalay
Thanks, i did.

σu=σv=σx^2+σy^2+2ρσxσx
one has a plus and the other a minus infront of the covariance term