Variance & Correlation Coefficient

[BLWFSOJ]

Hi all.

we have random variable Y=X1+X2. where Y,X1 and X2 are complex random variables.
any body knows what is the relation between the var(Y)
and correlation coefficient of (X1,X2)?

i appreciate you help.

regards,

 

[bulx]

probably difficult to generalize.

PDF of the sum of two random vars, if you know their joint PDF is
if Z = X + Y
fZ(z) = intg (from -inf to +inf)( fX,Y(z-y, y) dy

Then you could find variance as usual

e{Z^2} = intg (from -inf to +inf)( Z^2 fZ(z) dz

hmmm- that looks prob correct but too vague....if X, Y are jointly normal then Prices' theorem can be applied?

-b