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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!

james42
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Electro82
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1 Answers1

2

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.

André Nicolas
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