Random Variable - Random Signals and Processes Primer with MATLAB - page 149

Exercise M.2.8 (MATLAB file: exercise_M_2_8.m ). Generate the randomvariable:

Y ¼ ln X; (2.563)

where X is the uniform random variable in the range [0, 1]. Estimate PDF of
variable Y .
Solution The variable and its estimated density are shown in Fig. 2.80 .
Exercise M.2.9 (MATLAB file: exercise_M_2_9.m ). Generate the random vari-
able Y and estimate its PDF if

p

2ln X Y ¼ ; (2.564)

where X is the uniform random variable in the range [0, 1].
Solution The variable Y and its estimated density are shown in Fig. 2.81 .

10

8

6

4

2

0

0 100 200 300 400 500 600 700 800 900 1000

n

1

0.8
0.6

0.4
0.2

0

0 1 2 3 4 5 6 7 8 9 10

cells

Fig. 2.80 Transformation Y ¼ ln X , X is uniform in [0, 1]