Joint Probability Functions

[andrew2786]

Hi.
Here's the problem im not quite sure how to do:

The joint probability function f(x,y) of the discrete random variables X and Y are shown below.

X
______0____1_____2______3___
__1|(0.1)_(0.15)__(0.2)___(p)
Y_2|(p)___(0.15)_(0.15)_(0.05)
__3|(0.05)_(0)____(p)____(0)


Find the value of p
[ i do this and work it out as p=0.05]
Determine whether or not X and Y are independent
[ i do this by finding E(x)=1.4, E(Y)=1.6, E(XY)=2.2, then the Cov(X,Y)=-0.04 and as the covariance equals 0 when X and Y are independent, the variables show some degree of dependency]

Here's where my problem starts:
Evaluate P(X+Y=Z) for each possible values z of the random variable X+Y.

I don't know how to do this and would appreciate any help!

Thanks

Andy