Pascal Distribution (or Negative Binomial)

Notation:

$X \sim NB(r, p)$

Probability Mass Function:

$P(X=x)={x + r - 1 \choose r - 1} \cdot p^r(1-p)^x$

where:

Mean:

$\mathrm{E}[X]=\frac{r(1-p)}{p}$

Variance:

$\mathrm{Var}[X]=\frac{r(1-p)}{p^2}$

References:

  1. Pascal Distribution - Wikipedia
  2. Pascal Distribution - Wolfram MathWorld