Random Variable - Random Signals and Processes Primer with MATLAB - page 34

Fig. 2.6 The discrete random variable obtained from the continuous space

Fig. 2.7 The mixed random variable obtained from the continuous space

In the following example, we show that it is possible to obtain the mixed random
variable from a continuous space.
Example 2.1.5 Using the same continuous space from Example 2.1.3, the random
variable X ( s ) is defined in the following way, shown in Fig. 2.7 :

Xðs 0 Þ ¼ 0 ;

Xðs > 0 Þ ¼ x; 0 < x <a: (2.9)

In this example, the random variable is mixed because its range has one discrete
point and also a continuous part.