TITLE: Check answer, How to find Cov(x,y) and Var(2x-y)?
QUESTION [6 upvotes]: I have the following tableau
   x:   -1          0         1       total

y:  1    0         1/8        3/8      1/2
    2    3/8       1/8        0        1/2
total:   3/8       2/8        3/8       1

*)Find Cov(x,y) and Var(2x-y)
My work:
 I use Cov(x,y)= E(XY)-E(X)E(Y)
I have
 E(x)= 0
 E(Y)= 3/2
 E(X^2)= 3/4
 E(Y^2)= 5/2

After plug the values I have: 
   Cov(xy)=-15/8

And,
   var(2x-y)= 4 var(x) + var(y) - 2*2 cov(xy)
   Var(2x-y)= 10.75

Question: I solve the exercise ok, or I have some problem. I want to check. Thanks!

REPLY [2 votes]: You used a  correct formula for the covariance, but then you did not compute $E(XY)$.
This is $\sum_{x,y}xy\Pr(X=x, Y=y)$.  The computation is easy, since the table has many $0$'s.  It turns out that $E(XY)=-\frac{3}{8}$. Since $E(X)=0$  the covariance is $-3/8$.
The second computation is fine in outline, but uses the wrong value for the covariance. I can verify the answer after it is corrected.