I need to calculate the distribution function of the standard collectors' problem. I have to use generating functions so I have done this:
$$ G(z) = \frac{n}{n} z \frac{1}{1-\frac{1}{n} z} \frac{n-1}{n} z \frac{1}{1-\frac{2}{n} z} \frac{n-2}{n} z \frac{1}{1-\frac{3}{n} z} \frac{n-3}{n} z \cdots \frac{1}{1-\frac{n-1}{n} z} \frac{n-(n-1)}{n} z $$
Now if I want to know $P(X = m)$ I need to extract the m-th term of the generating function but I don't know how.
Thanks!!!