Geometric Distribution

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Definition

Geometric Distribution

The geometric distribution models the number of attempts before (or until) a success with probability $p$.

Probability Mass Function

The pmf is given by:

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

Expected Value

The expected value is given by:

$$\mathbb{E}[X]=\frac{1-p}{p}$$

Variance

The variance is given by:

$$\mathbb{V}ar(X)=\frac{1-p}{p^2}$$