Probability Distribution Function and Shape

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The Discrete Uniform Distribution

The discrete uniform distribution on the set of integers {1,2,3,..., N } gives probability 1/ N to

each element of this set. This distribution is denoted by Discrete Uniform ( N ).

Hence, the probability distribution function will be constant at f ( x ) = 1/ N , x in {1,2,3,..., N },

and the cumulative distribution function is given by

0, if x <1

F ( x ) = [ x ]/ N , if 1<= x <= N

1, if x > N ,

where [ x ] denotes the greatest integer function (also known as the "floor" function).

If X is the value showing on a roll of a fair six-sided die, then X has the discrete uniform distribution

on the set {1,2,3,4,5,6}. The following Maple code will form a list consisting of the distribution of X .

> DiscUnif_6:=[1,1/6,2,1/6,3,1/6,4,1/6,5,1/6,6,1/6];

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The following Maple code will make a probability histogram for the distribution of X .

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> ProbHist(DiscUnif_6);

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