Geometric equations

· Format:

Geometric(p)

· Probability mass function:

$\begin{array}{l}\displaystyle f(x)=p(1-p)^{x-1}\end{array}$

· Cumulative distribution function:

$\begin{array}{l}\displaystyle F(x)=1-(1-p)^x\end{array}$

· Parameter restrictions:

$\begin{array}{l}\displaystyle 0< p \leq 1\end{array}$

· Domain:

x = {1, 2, 3,...}

· Mean:

$\begin{array}{l}\displaystyle \frac{1}{p}\end{array}$

· Mode:

1

· Variance:

$\begin{array}{l}\displaystyle \frac{1-p}{p^2}\end{array}$

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