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Math Help - Exponential question in conditional probability

  1. #1
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    Exponential question in conditional probability

    The p.g.f of a random variable is:
     G_T(x) = exp^{n \theta(x-1)}

    This seems to simplify to:
    f(x|\theta) = \frac{exp^{-n \theta}.\theta^t}{\prod x_i!} where t = \sum x_i

    But this means  exp^{n \theta t} = \frac{\theta^t}{ \prod x_i!} ,
    which doesn't look right.

    Not sure how the f(x|\theta) equation is derived.
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  2. #2
    MHF Contributor matheagle's Avatar
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    where did these x_i! come from?
    and is x>1???
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