Random Variable - Random Signals and Processes Primer with MATLAB - page 38

This distribution is plotted in Fig. 2.9 .
In the following example, we can see the distribution of a continuous random
variable.

Example 2.2.3 Consider the continuous random variable X defined in the continuous
interval [ a , b ], as shown in Fig. 2.10a for a ¼ 2and b ¼ 6.
Solution For the interval of 6 x <1 , we have:

PfX xg¼ 1

6 x <1:

for (2.27)

For the interval 2 x < 6, the probability PfX xg depends on the ratio of
the ( x 2) and the total width (6 2),

x 2
4

PfX xg¼ for 2 x < 6 : (2.28)

Fig. 2.9 Illustration of the distribution in Example 2.2.2

Fig. 2.10 Illustration of the distribution in Example 2.2.3