Normal Random Variable - Random Signals and Processes Primer with MATLAB - page 280

2 =4

m=1, s

6

4

2

0

- 2

- 4

0 100 200 300 400 500

n

600 700 800 900 1000

Fig. 4.32 Random variables in Exercise M.4.4

(b) The probability P 1 is illustrated in Fig. 4.33 , indicating that the probability is the
area below the PDF in the range [ 1 , 3] and also it is the value of the
distribution function for x ¼ 3.
The probability P 2 is:

P 2 ¼ 0 : 3085 : (4.233)

The probability P 2 is related with the PDF and distribution as shown in
Fig. 4.34 .
Exercise M.4.5 (MATLAB file: exercise_M_4_5.m ). Find the probability that the
random variable X ¼ N (2, 9) is in the interval [ 1, 5] and show this probability in
the PDF and distribution plots.

Solution The random variable along with the interval (dotted line), where the
desired probability being looked for, is shown in Fig. 4.35 .
The desired probability is obtained from the erf function:

P 21 ¼ 0 : 1587 ; (4.234)

P 22 ¼ 0 : 8413 ; (4.235)

P 22 P 21 ¼ 0 : 682 : (4.236)