Random Processes - Random Signals and Processes Primer with MATLAB - page 416

Solution The process is generated using the MATLAB code X ¼ (R2 R1)*rand
(M,N) + R1 ; where R1 ¼ 1 and R2 ¼ 1.

(a) The random variables are shown in Fig. 6.16 for the first n ¼ 1,000 samples.
(b) The mean values are estimated using the MATLAB file mean.m. The following
mean values are obtained:

m 1 ¼ 0 : m 2 ¼ 0 : m 3 ¼ 0 : :

0065 ; 0028 ; 0055 (6.240)

All estimated mean values are approximately equal to the mathematical mean
value which is equal to zero, m ¼ 0.
(c) The variances are estimated using the MATLAB file var.m and the following
values for the variances are obtained:

s 1 ¼ 0 s 2 ¼ 0 s 3 ¼ 0 : : : :

3333 ; 3357 ; 3336 (6.241)

The estimated variances are approximately equal to the mathematical value of
the variance which is s 2 ¼ 0.3333.

(d) The histograms are shown in Fig. 6.17 .
The histograms from Fig. 6.17 indicate that all three variables are uniform in
[ 1, 1].

1

0

- 1 0

200 400 600 800 1000

n

1

0

- 1

0 200 400 600 800 1000

n

1

0

- 1

0 200 400 600 800 1000

n

Fig. 6.16 Random variables X 1 , X 2 , and X 3 in Exercise M.6.1