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