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