ThmDex – An index of mathematical definitions, results, and conjectures.
F13508
Formulation 3
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 $G \in \text{Random} \{ 0, 1, 2, \ldots \}$ is a cogeometric random natural number with parameter $\theta$ if and only if \begin{equation} G \overset{d}{=} \max \left\{ N \in \{ 0, 1, 2, \ldots \} : \sum_{n = 1}^N X_n \neq 1 \right\} \end{equation}