Graphics Programs Reference
In-Depth Information
Uniform Distribution
A
uniform distribution
or
rectangular distribution
is a distribution that
has constant probability (Fig. 3.4). The corresponding probability density
function is
where the random variable
x
has any of
N
possible values. The cumulative
distribution is
The probability density function is normalized to unity
i.e., the sum of probabilities is one. Therefore, the maximum value of the
cumulative distribution is one as well.
Probability Density
Function
Cumulative Distribution
Function
0.2
1.2
f(x)=1/6
1
0.15
0.8
0.1
0.6
0.4
0.05
0.2
0
0
123456
0123456
x
x
a
b
Fig. 3.4 a
Probability density function
f
(
x
) and
b
cumulative distribution function
F
(
x
)
of a uniform distribution with
N
=6. The 6 discrete values of the variable
x
have the same
probability 1/6.