Page 43 - Computational Statistics Handbook with MATLAB

Chapter 2: Probability Concepts 29

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Perhaps one of the most important distributions is the uniform distribution
for continuous random variables. One reason is that the uniform (0, 1) distri-
bution is used as the basis for simulating most random variables as we dis-
cuss in Chapter 4.
A random variable that is uniformly distributed over the interval (a, b) fol-
lows the probability density function given by
1
(
,
f xa b) = -----------; a < x < . b (2.27)
;
b – a
The parameters for the uniform are the interval endpoints, a and b. The mean
and variance of a uniform random variable are given by
a + b
EX[] = ----------- ,
2

and

( b – a) 2
VX() = ------------------ .
12

The cumulative distribution function for a uniform random variable is

 0; x ≤ a
 x – a
Fx() =  -----------; a < x < b (2.28)
 b – a
 1; x ≥ b.

Example 2.4
In this example, we illustrate the uniform probability density function over
the interval (0, 10), along with the corresponding cumulative distribution
function. The MATLAB Statistics Toolbox functions unifpdf and unifcdf
are used to get the desired functions over the interval.

% First get the domain over which we will
% evaluate the functions.
x = -1:.1:11;
% Now get the probability density function
% values at x.
pdf = unifpdf(x,0,10);
% Now get the cdf.
cdf = unifcdf(x,0,10);

© 2002 by Chapman & Hall/CRC