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.
