SEEM 4480 Decision Methodology and Applicatons
Xuedong He, Fall 2017
Suggested Solution to Homework 3
1.
(a) Given that Ms.
Jones apply for both jobs, denote
A
as the event that
Ms. Jones will be accepted for the first job and
B
as the event that she
will be accepted for the second job. Denote
P
as the probability measure
that represents Ms. Jones’ subjective belief. Then, we have
P
(
A
) = 0
.
7,
P
(
B
) = 0
.
5, and
P
(
B

A
) = 0
.
6. We want to compute
P
(
A
∪
B
). Denote
¯
B
as the complement to
B
.
(b) If Ms. Jones applies the third job, she feels that the probability of getting
the job is 0.7. If she applies the first two jobs, she feels that the probability
of getting at least one of them is 0.78. Thus, she should apply for the first
two jobs.
2. Denote
N
for normal and
A
for abnormal. Then, the diagram reveals that
P
(
x
1
= 1

N
) = 0
.
2
,
P
(
x
1
= 0

N
) = 0
.
8
,
P
(
x
2
= 2

N, x
1
= 1) = 0
.
2
,
P
(
x
2
= 1

N, x
1
= 1) = 0
.
3
,
P
(
x
2
= 0

N, x
1
= 1) = 0
.
5
,
P
(
x
1
= 1

A
) = 0
.
7
,
P
(
x
1
= 0

A
) = 0
.
3
,
P
(
x
2
= 2

A, x
1
= 1) = 0
.
7
,
P
(
x
2
= 1

A, x
1
= 1) = 0
.
2
,
P
(
x
2
= 0

A, x
1
= 1) = 0
.
1
.
(b) Following this rule, a normal is misclassified as an abnormal if and only if
a normal is classified as 1 on measurement 1 and as 1 on measure 2. Thus,
1
SEEM 4480 Decision Methodology and Applicatons
Xuedong He, Fall 2017