Definition:Hat-Check Distribution

Definition
Let $X$ be a discrete random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \set {0, 2, 3, \ldots, n}$

Let $X$ represent the number of elements in a a totally ordered set with $n$ elements that are not in the correct order.

Then $X$ has the Hat-Check distribution with parameter $n$ (where $n > 0$) :

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