| Discrete uniform distribution | CDF | ⌊ k ⌋ − a + 1 n {\displaystyle {\frac {\lfloor k\rfloor -a+1}{n}}} | 1.00 | infobox |
| Discrete uniform distribution | CF | e i a t − e i ( b + 1 ) t n ( 1 − e i t ) {\displaystyle {\frac {e^{iat}-e^{i(b+1)t}}{n(1-e^{it})}}} | 1.00 | infobox |
| Discrete uniform distribution | Entropy | ln ( n ) {\displaystyle \ln(n)} | 1.00 | infobox |
| Discrete uniform distribution | Excess kurtosis | − 6 ( n 2 + 1 ) 5 ( n 2 − 1 ) {\displaystyle -{\frac {6(n^{2}+1)}{5(n^{2}-1)}}} | 1.00 | infobox |
| Discrete uniform distribution | Mean | a + b 2 {\displaystyle {\frac {a+b}{2}}} | 1.00 | infobox |
| Discrete uniform distribution | Median | a + b 2 {\displaystyle {\frac {a+b}{2}}} | 1.00 | infobox |
| Discrete uniform distribution | MGF | e a t − e ( b + 1 ) t n ( 1 − e t ) {\displaystyle {\frac {e^{at}-e^{(b+1)t}}{n(1-e^{t})}}} | 1.00 | infobox |
| Discrete uniform distribution | Mode | N/A | 1.00 | infobox |
| Discrete uniform distribution | Notation | U { a , b } {\displaystyle {\mathcal {U}}\{a,b\}} or u n i f { a , b } {\displaystyle \mathrm {unif} \{a,b\}} | 1.00 | infobox |
| Discrete uniform distribution | Parameters | a , b {\displaystyle a,b} integers with b ≥ a {\displaystyle b\geq a} n = b − a + 1 {\displaystyle n=b-a+1} | 1.00 | infobox |
| Discrete uniform distribution | PGF | z a − z b + 1 n ( 1 − z ) {\displaystyle {\frac {z^{a}-z^{b+1}}{n(1-z)}}} | 1.00 | infobox |
| Discrete uniform distribution | PMF | 1 n {\displaystyle {\frac {1}{n}}} | 1.00 | infobox |
| Discrete uniform distribution | Skewness | 0 {\displaystyle 0} | 1.00 | infobox |
| Discrete uniform distribution | Support | k ∈ { a , a + 1 , … , b − 1 , b } {\displaystyle k\in \{a,a+1,\dots ,b-1,b\}} | 1.00 | infobox |
| Discrete uniform distribution | Variance | ( b − a + 1 ) 2 − 1 12 {\displaystyle {\frac {(b-a+1)^{2}-1}{12}}} | 1.00 | infobox |
| Discrete uniform distribution | is a | symmetric probability distribution wherein each of some finite whole number n of outcome values are equally likely to be observed | 0.90 | text |
