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Probability generating function

  1. Nov 28, 2009 #1
    1. The problem statement, all variables and given/known data

    A random variable X has the generating function
    f(z) = 1 / (2-z)^2
    Find E(X) and Var(X).


    2. Relevant equations



    3. The attempt at a solution

    Would anyone explain in simpler terms the notion of the generating function, such that I may be able to solve problems? All I have found were proofs, but nothing of practical use.

    Thank you very much!
     
  2. jcsd
  3. Nov 28, 2009 #2
    Thank you very much, LC!

    I imagine that there isn't any significant difference between MGF and PGF (probability), the latter being a special application of the first?!
    If so, I still have a couple of questions:
    1) Do the formulae apply to all sorts of probability distributions/densities?
    2) How do I calculate the variance (formula-wise) for these generating functions (which I understand are not really functions but series of terms)?

    Thank you very much in advance.
     
  4. Nov 28, 2009 #3

    LCKurtz

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    I posted that reply quickly as I was about to leave for a movie and hadn't noticed you were asking about a probability generating function instead of moment generating function. I deleted the post but apparently you saw it before I deleted it. PGF's are defined for non-negative integer valued random variables. For a PGF PX(z),

    E(X) = P'X(1) and
    Var(X) = P''X(1) + P'X(1) - (P'X(1))2
     
    Last edited: Nov 28, 2009
  5. Nov 29, 2009 #4
    Thank you very much, LC!
    I hope I find you around again when I cry for help.
     
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