Definition:Hat-Check Distribution/Definition 2

Definition

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

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

where:

$!k$ is the subfactorial of $k$

$\dbinom n k$ 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