# Generating function expectation

1. Apr 19, 2007

### 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?

2. Apr 19, 2007

### Hurkyl

Staff Emeritus
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.