DiscreteUniformDistribution

The discrete uniform distribution on the integers $\{min, \ldots, max\}$ .

DiscreteUniformDistribution({min, max})an inert distribution object — Wolfram's own call shape, a single two-element list.

Typed signatures

Type	Package	Applies
`(list<integer>) -> distribution`	`statistics`	always

Domain: Statistics

Details

$PDF(k) = 1/(max-min+1)$ — no bounds check outside $\{min,\ldots,max\}$ (a documented divergence).
$CDF(x) = (\lfloor x\rfloor - min + 1)/(max-min+1)$ , clamped to $0$ below $min$ and $1$ above $max$ .
$Mean = (min+max)/2$ , $Variance = ((max-min+1)^2-1)/12$ , both exact.
RandomVariate draws $min + \lfloor U \cdot (max-min+1)\rfloor$ .