Discrete Uniform Distribution
Acme Limited is a car manufacturer. The company can paint the car in 3 possible colors: White, Black and Blue. Until the population is sampled, the company does not know the demand for each color. Until such time, the company should assume that probability of demand for each color equals one-third.
If White, Black and Blue denote the events "Demand for White/Black/Blue car"
P(White) = P(Black) = P(Blue) = 1/3.
The Standard Discrete Uniform Distribution is obtained by representing events E1, E_{2}, ....., E_{K} by the numbers 1, 2, ....., K.
(Remember, a random variable must assume numerical values.)
In the above example
Event
X
P(X)
White
1
1/3
Black
2
Blue
3
It can be shown for the Standard Discrete Uniform Distribution
m = E(X) = (K + 1)/2
s^{2} = V(X) = (K^{2} - 1)/12