## ABSTRACT

The random variable, X, has a uniform distribution if f(x) is given by

( ) 1 ( )f x a x b

b a = ≤ ≤

− (4.1)

Figure 4.1 shows the probability density function, f(x), for the uniform distribution.

The cumulative distribution function, F(x), for the uniform distribution is given by

( ) ( )x aF x a x b

b a −

= ≤ ≤ −

(4.2)

The mean, E[X], and the variance, Var[X], for the uniform distribution are given by

2 a b

E X +

=

(4.3)

and

12 b a

Var X −

=

(4.4)

respectively.