Other Important Random Variables - Random Signals and Processes Primer with MATLAB - page 365

PROBABILITY P1

0.8

0.6

P1

0.4

0.2

0 0

1 2 3 4 5 6 7 8 9 10

Range

PROBABILITY P1, P1=F(A)

1

P1

0.5

0

0 2 4 6 8 10 12

Range

Fig. 5.46 Illustration of the probability P 1

The probability P 2 is illustrated in Fig. 5.47 .

P 2 ¼ Pf 0 : 5 <X 2 g¼ 0 : 4684 :

5.11 Questions

Q.5.1. Explain why a Rician variable approaches to a Rayleigh variable in the case
of a small values of A related to a deviation s ( A s )?
Q.5.2. Explain why a Rician variable approaches to a Gaussian variable for high
values of A related to a deviation s ( A s )?
Q.5.3. When does a lognormal variable approach a normal variable?
Q.5.4. There are k events in a Poisson flow of events in the random time interval t .
Which random variable can describe the random interval t ?
Q.5.5. Why is a Poisson random variable said to be a “rare events variable?”
Q.5.6. (a) Which random variable has an equal mean value and standard deviation?
(b) Which random variable has an equal mean value and variance?