covariance

vinux

Dark Knight
#2
I know that COV(aX,bY)=ab COV(X,Y)

But I dont know how to solve this : COV(aX,bY+cX)

anyone can help me ?
Cov(X,Y) = E[X*Y] - E[X]*E[Y]
COV(aX,bY+cX)=E[aX*(bY+cX)] - E[aX]*E[(bY+cX)]
= abE[XY] + acE[X*X] - abE[X]E[Y] - acE[X]E[X]
= abE[XY] - abE[X]E[Y] + acE[X*X] - acE[X]E[X]
=abCov(X,Y) + acVar(X)

Rgds
VinuX