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Generating function expectation

  1. Apr 19, 2007 #1
    A probability distribution,[tex]f(x) [/tex] ,can be represented as a generating function,[tex]G(n) [/tex], as [tex] \sum_{x} f(x) n^x [/tex]. The expectation of [tex]f(x) [/tex] can be got from [tex] G'(1) [/tex].

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

    Now my question is how can I get the expectation of [tex] f(x,y) [/tex] from the above generating function?
  2. jcsd
  3. Apr 19, 2007 #2


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    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.
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