Transformations of Discrete RVs

[dogma]

Hello out there,

I have a question about the transformation of discrete random variables.

I have a joint pdf given by:

$$f(x,y)=\frac{(x-y)^2}{7}$$ where x = 1, 2 and y = 1, 2, 3

I can easily create a table summarizing the joint pdf of RVs X and Y, f(x,y). I now have a transformation of U = X + Y and V = X - Y.

I'm not quite sure how to go about creating a table to summarize the joint pdf of U and V.

To my feeble mind, it appears that u = 2, 3, 4, 5 and v = -2, -1, 0, 1 (with some numbers for u and v repeated).

How would I go about using u and v and the probabilities from the f(x,y) table to create (transform) the joint pdf, f(u,v)?

I would greatly appreciate someone pointing me in the right direction (i.e. a good, swift kick in the rear). I apologize in advance if some of my terminology is incorrect.

Thanks a bunch,

dogma

 

[dogma]

Well...all's well...figured it out.