This distribution assigns equal probabilities to all possible values of the random variable within the range a to b, inclusive. It is often used when only the range is known, but there is no information about the distribution within the range.

We use the general expression for the variance, because there is no simple expression that uses only a and b.

Example: : A computer is shipped with several identical parts. A company that assembles computers is interested in the distribution of the number of parts required. No statistics are available, however, the design of the computer assures that every computer requires at least 1 part and the most that can be installed is six parts. With no other information, we assume that all possibilities are equally likely. This is modeled by the uniform distribution.