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.