Discrete Uniform Random Variable

A Random Variable $X$ is said to have a discrete uniform distribution on integers $a,a+1,...,b$ if $P(X=k)=\frac{1}{b-a+1}$

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Properties:

A Random Variable $X$ with a discrete uniform distribution on integers $a,a+1,...,b$ has:

Name	Property	Value
Expected Value	$\mathbb{E}(X)$	$\frac{a+b}{2}$
Variance	$Var(X)$	$\frac{(b-a+1{)}^2}{12}$