A Friendly Introduction for Electrical and Computer Engineers
Edition 2
Roy D. Yates and David J. Goodman
Problem Solutions
: Yates and Goodman,
1.2.1 1.2.2 1.2.4 1.3.1 1.3.2 1.3.4 1.4.1 1.4.4
1.5.2 and 1.5.3
Problem 1.2.1 Solution
(a) An outcome specifes whether the Fax is high (
h
), medium (
m
), or low (
l
) speed, and
whether the Fax has two (
t
) pages or Four (
f
) pages. The sample space is
S
=
{
ht, hf, mt, mf, lt, lf
}
.
(1)
(b) The event that the Fax is medium speed is
A
1
=
{
mt, mf
}
.
(c) The event that a Fax has two pages is
A
2
=
{
ht, mt, lt
}
.
(d) The event that a Fax is either high speed or low speed is
A
3
=
{
ht, hf, lt, lf
}
.
(e) Since
A
1
∩
A
2
=
{
mt
}
and is not empty,
A
1
,
A
2
, and
A
3
are not mutually exclusive.
(F) Since
A
1
∪
A
2
∪
A
3
=
{
ht, hf, mt, mf, lt, lf
}
=
S,
(2)
the collection
A
1
,
A
2
,
A
3
is collectively exhaustive.
Problem 1.2.2 Solution
(a) The sample space oF the experiment is
S
=
{
aaa, aaf, afa, faa, ffa, faf, aff, fff
}
.
(1)
(b) The event that the circuit From
Z
Fails is
Z
F
=
{
aaf, aff, faf, fff
}
.
(2)
The event that the circuit From
X
is acceptable is
X
A
=
{
aaa, aaf, afa, aff
}
.
(3)
(c) Since
Z
F
∩
X
A
=
{
aaf, aff
} 6
=
φ
,
Z
F
and
X
A
are not mutually exclusive.
(d) Since
Z
F
∪
X
A
=
{
aaa, aaf, afa, aff, faf, fff
} 6
=
S
,
Z
F
and
X
A
are not collectively
exhaustive.
1