• June 22nd 2011, 05:44 AM
FGT12
Find the generating function of the following mass function, and state where it converges.

$f(m)=\binom{n+m-1}{m}{p}^n{1-p}^m$ for m is greater or equal to 0

I get:

$G_X(s)=\sum_{i=1}^{\infty} s^i \binom{n+m-1}{m}{p}^n{1-p}^m$

However I have no idea how to evaluate the sum
• June 22nd 2011, 08:26 AM
theodds
\begin{align*}G(s) &= \sum_{m = 1} ^ \infty s^m \binom{n + m - 1}{m}p^n (1 - p)^m \\ &= \sum_{m = 1} ^ \infty \binom{n + m - 1}{m} p^n [s (1 - p)]^m \end{align*}