# Thread: Exponential question in conditional probability

1. ## 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.

2. where did these $x_i!$ come from?
and is x>1???