Random Variable - Random Signals and Processes Primer with MATLAB - page 144

From Example 2.6.1 and ( 2.555 ), we have:

<

1
4 2 ¼

1
2

for 2 < y < 4 ;

f Y ðyÞ ¼ (2.556)

:

0 otherwise :

The random variable and its estimated PDF are shown in Fig. 2.74 .

Exercise M.2.3 (MATLAB file: exercise_M_2_3.m ). Using the MATLAB file
rand.m which generates the uniform random variable X in the interval [0, 1],
write the MATLAB program to generate the uniform variable in the desired interval
[ R 1 , R 2 ]. Consider, for example, R 1 ¼ 2 and R 2 ¼ 4.
Solution Using the result of Example 2.6.4, we have:

Y ¼ ðR 2 R 1 ÞX þ R 1 :

(2.557)

The corresponding MATLAB file is unif.m. The transformed variable Y and its
estimated PDF are shown in Fig. 2.75 .

Exercise M.2.4 (MATLAB file: exercise_M_2_4.m ). Estimate and plot the PDF
and distribution of the uniform random variable X in the interval [0.5, 3.5].

5

4

3

2

1

100 200 300 400 500

n

600 700 800 900

0.8

0.6

0.4

0.2

0

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

cells

Fig. 2.74 Transformed uniform variable and its estimated PDF