Uniform Distribution. The discrete Uniform distribution (the term first used by Uspensky, 1937) has density function:

f(x) = 1/N          x = 1, 2, ..., N

The continuous Uniform distribution has density function: where

f(x) = 1/(b-a)        a < x < b

a     is the lower limit of the interval from which points will be selected
b     is the upper limit of the interval from which points will be selected