# Covariance of Discrete Random Variables

1. Apr 8, 2009

### Shackman

1. The problem statement, all variables and given/known data
Find E(XY), Cov(X,Y) and correlation(X,Y) for the random variables X, Y whose joint distribution is given by the following table.

X
1 2 3
Y -1| 0 .1 .1

0| 0 .5 .6

1| .2 0 0

3. The attempt at a solution

The covariance and correlation fall into place quite easily once I have found E(XY). I have found E(X), E(Y), Var(X) and Var(Y) but none of these values help as the variables are not independent. So in trying to find E(XY), I am trying to set up the double integral, but am confused by the fact that the variables are discrete. The limits of integration are not obvious and it is not obvious how to integrate a discrete function either. Is there another way I can look at this?

Last edited: Apr 8, 2009
2. Apr 8, 2009

### Billy Bob

$$E[XY]=\sum\sum xyf(x,y)$$

3. Apr 9, 2009

### Shackman

That is so much better. Thanks. The organization of my book is pretty terrible, I'm just finding that equation now.