\begin{definition}[Definition:Hat-Check Distribution/Definition 1]
$X$ has the '''hat-check distribution with parameter $n$''' {{iff}}:
:$\ds \map \Pr {X = k} = \dfrac 1 {\paren {n - k }!} \sum_{s \mathop = 0}^k \dfrac {\paren {-1}^s} {s!}$
\end{definition}