Let $X_1, X_2, X_3, \dots \in \text{Bernoulli}(\theta)$ each be a D207: Bernoulli random boolean number such that

(i)	$X_1, X_2, X_3, \dots$ is an D2713: Independent random collection
(ii)	$\theta \in (0, 1]$

A D5748: Random positive integer $G \in \text{Random} \{ 1, 2, 3, \ldots \}$ is a geometric random positive integer with parameter $\theta$ if and only if \begin{equation} G \overset{d}{=} \min \left\{ N \in \{ 1, 2, 3, \ldots \} : \sum_{n = 1}^N X_n = 1 \right\} \end{equation}