Chapter 5
Random Signals and Noise
5.1
Problem Solutions
Problem 5.1
The various sample functions are as follows. Sample functions for case (a) are horizontal
lines at levels
A,
0
,
−
A
, each case of which occurs equally often (with probability 1/3).
Sample functions for case (b) are horizontal lines at levels
5
A,
3
A, A,
−
A,
−
3
A,
−
5
A
,
each case of which occurs equally often (with probability 1/6). Sample functions for case
(c) are horizontal lines at levels
4
A,
2
A,
−
2
A,
−
4
A,
or oblique straight lines of slope
A
or
−
A
, each case of which occurs equally often (with probability 1/6).
Problem 5.2
a. For case (a) of problem 5.1, since the sample functions are constant with time and
are less than or equal 2A, the probability is one. For case (b) of problem 5.1, since
the sample functions are constant with time and 4 out of 6 are less than or equal to
2A, the probability is 2/3. For case (c) of problem 5.1, the probability is again 2/3
because 4 out of 6 of the sample functions will be less than
2
A
at
t
= 4
.
b. The probabilities are now 2/3, 1/2, and 1/2, respectively.
c. The probabilities are 1, 2/3, and 5/6, respectively.
Problem 5.3
a. The sketches would consist of squarewaves of random delay with respect to
t
= 0
.
1