Random Variable - Random Signals and Processes Primer with MATLAB - page 86

The result ( 2.260 ) may be generalized to include any continuous range of the
random variable:

1

m ¼ EfXg¼ xf X ðxÞ d x: (2.261)

1

Example 2.7.7 Find the mean values of the random variables X 1 and X 2 with the
corresponding density functions shown in Fig. 2.41 :

(

1 = 2 for 1 x 1 ;

f X 1 ðxÞ¼

:

0 otherwise

(

(2.262)

=

0 x 2

;

1 2 for

f X 2 ðxÞ¼

0 otherwise :

Solution From ( 2.261 ), we have:

ð

1

1
2 d x ¼

1
4

1
4 ¼ 0

m X 1 ¼ x ;

1

(2.263)

ð

2

2 2
4 0 ¼ 1

1
2 d x ¼

m X 2 ¼ x :

0

Example 2.7.8 We want to find the mean value of the random variable X with the
density function, shown in Fig. 2.42 .
The density function is described as:

8
<
:

1
4 ðx þ 2 Þ

for 2 x 0 ;

f X ðxÞ¼ (2.264)

1
4 ðx 2 Þ

0 x 2

:

for

Fig. 2.41 Density functions in Example 2.7.7