\begin{definition}[Definition:Geometric Distribution/Formulation 1]
Let $X$ be a discrete random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
$X$ has the '''geometric distribution with parameter $p$''' {{iff}}:
:$\map X \Omega = \set {0, 1, 2, \ldots} = \N$
:$\map \Pr {X = k} = \paren {1 - p} p^k$
where $0 < p < 1$.
It is written:
:$X \sim \Geometric p$
\end{definition}