Random Variable - Random Signals and Processes Primer with MATLAB - page 142

2.10 MATLAB Exercises

Exercise M.2.1 (MATLAB file: exercise_M_2_1.m ). Show that the linear
transformation of the uniform random variable results in a uniform variable,
using as an example, the uniform random variable X in the interval [0, 1] and the
transformation:

Y ¼ 2 X þ 3 : (2.550)

Solution The random variables X and Y are shown in Fig. 2.72 .

We can easily note that the variable Y is also uniform but in a different interval
(i.e., in the interval [1, 3]) as presented in the numerical Example 2.6.1.
From ( 2.550 ), we have:

X ¼ x 1 ¼ 0 ; Y ¼ y 1 ¼ 3 ; (2.551)

X ¼ x 2 ¼ 1 Y ¼ y 2 ¼ 1 : (2.552)

;

Uniform r.v., [0,1]

4
3

2

1

0

− 1

0 100 200 300 400 500 600 700 800 900 1000

Y= − 2X+3

4

3

2
1

0

− 1

0 100 200 300 400 500 600 700 800 900 1000

n

Fig. 2.72 Random variables X and Y