Discrete Geometric Distribution

A kind of Discrete Distribution that models the number of independent Bernoulli Trials until the first Success, where each trial has a Probability $p$ of success.

$$X\sim \text{Geometric}(p)$$

• $f(x)=p{q}^{x-1}\text{for }x\in {\mathbb{Z}}^{+}$
• $E(X)=\frac{1}{p}$
• $\text{Var}(X)=\frac{1}{p}\left(\frac{1}{p}-1\right)=\frac{q}{p^2}$