Covariance, results
Summary
X,Y,Z
are random variables and
a,b
are constants.
-
Cov(X,Y)=E(XY)−E(X)E(Y)
-
If
X
and
Y
are independent then
Cov(X,Y)=0
. The opposite is not true.
-
If
X
and
Y
are normally distributed and
Cov(X,Y)=0
then
X
and
Y
are independent
-
Cov(X,X)=Var(X)
-
Cov(X,a)=0
-
Cov(X,Y)=Cov(Y,X)
-
Cov(X+Y,Z)=Cov(X,Z)+Cov(Y,Z)
-
Cov(aX,bY)=abCov(X,Y)
-
Var(X+Y)=Var(X)+Var(Y)+2Cov(X,Y)