Definition:Hat-Check Distribution/Definition 1

Definition

$X$ has the hat-check distribution with parameter $n$ if and only if:

$\ds \map \Pr {X = k} = \dfrac 1 {\paren {n - k }!} \sum_{s \mathop = 0}^k \dfrac {\paren {-1}^s} {s!}$

Also see

• Equivalence of Definitions of Hat-Check Distribution
• Hat-Check Distribution Gives Rise to Probability Mass Function satisfying $\map \Pr \Omega = 1$.

• Definition:Hat-Check Triangle