Definition:Hat-Check Distribution/Definition 2

Definition
$X$ has the hat-check distribution with parameter $n$ :


 * $\ds \map \Pr {X = k} = \dfrac {!k} {n! } \dbinom n k$

where $!k$ is the subfactorial of k and $\dbinom n k$ is the binomial coefficient

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