Geometric Distribution

A special case of the negative binomial distribution, where $r=1$. Denoted by $g^*(x;p)$. Memoryless.

$$P(x) = p(1-p)^{x-1}$$

Here:

• $p$ - probability of success in a single trial

Mean

$$\mu_X = \frac{1}{p}$$

Variance

$$V_x = \frac{1-p}{p^2}$$