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

f(x) = 1/N, for x = 1, 2, ..., N

The continuous uniform distribution has density function:

f(x) = 1/(

where

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 |