Generating function expectation

[jimmy1]

A probability distribution,$$f(x)$$ ,can be represented as a generating function,$$G(n)$$, as $$\sum_{x} f(x) n^x$$. The expectation of $$f(x)$$ can be got from $$G'(1)$$.

A bivariate generating function, $$G(m,n)$$ of the joint distribution $$f(x,y)$$ can be represented as $$\sum_{x} \sum_{y} f(x,y) n^x m^y$$.

Now my question is how can I get the expectation of $$f(x,y)$$ from the above generating function?

 

[Hurkyl]

Er, are you sure you're asking the right question? What meaning did you have in mind for "the expectation of f(x, y)"? Do you mean to think of f as the probability distribution for an R²-valued random variable, or something like that? Anyways, I would start by writing down the definition of expected value, and work from there.