José Rizal University
Graduate School
Master in Public Administration Program
Exercises: Decision Making
Using Probability I
Presented to Mr. Rodolfo B. Gaerlan
Faculty Adviser
In Partial Fulfillment of
the Requirements of the Course
Subject: Statistics & Quantitative Analysis
By Group I:
John Ko, Amor Sande and Jesus Boadilla
2nd Trimester / School Year 2005-2006
Exercise 4-6
Solution:
(a) 25 units of stock
Conditional profit
30
50
50
50
Probability
x
0.1
x
0.3
x
0.5
x
0.1
Total
Expected profit
3
15
25
5
Probability
x
0.1
x
0.3
x
0.5
x
0.1
Total
Expected profit
-4
-6
20
12
$ 48
(b) 60 units of stock
Conditional profit
-40
-20
40
120
$ 22
(c) Probability for which the maximizing equation is true
P = ML ÷ (MP + ML) = $2 ÷($2+$2) = 0.5
check the cumulative probability, we find 60 units to be
bought will have 0.6 of probability which is slightly bigger
than 0.5, therefore, 60 units of stocks should be bought.
(d) Expected value of perfect information
Conditional profit
40
50
80
120
Probability
x
0.1
x
0.3
x
0.5
x
0.1
Total
Expected profit
4
15
40
12
$ 71
Exercise 4-9
Solution:
(1) p=0.4 1-p=0.6
Expected profit to the beach:
80 x 0.4 + 10 x 0.6 = $38
Expected profit to stay home:
40 x 0.4 + 35 x 0.6 = $37
Since expected profits of $38 is bigger than that
of $37; therefore, it is recommended to drive to
the beach rather then stay home.
(2) Perfect information value:
80 x 0.4 + 35 x 0.6 = $53
and expected profit is $38
Therefore, he can pay $15 ($53-$38) for a
perfect information.
Exercise 4-21
Solution:
Find the cumulative probability:
Pounds demanded
20
21
22
23
24
25
26
27
28
29
30
Probability
0.10
0.12
0.13
0.12
0.11
0.10
0.09
0.08
0.07
0.05
0.03
Cumulative probability
1.00
0.90
0.78
0.65
0.53
0.42
0.32
0.23
0.15
0.08
0.03
Probability for which the maximizing equation
P = ML ÷ (MP + ML) = 27 ÷(37+27) = 0.422
Check with cumulative probability, then we find
out that the cumulative probability of 24 pounds
demanded at 0.53 is slightly bigger than 0.422,
therefore, we can say that the optimal stocking
decision will be 24 pounds.
Exercise 4-28
Solution:
Utility of 20,000 = 0.9(10) + 0.1(0) = 9
Utility of 10,000 = 0.8(10) + 0.2(0) = 8
Utility of -10,000 = 0.4(10) + 0.6(0) = 4
10 5
9
4
8
3
7
2
6
1
5
0
4
-1
3
-2
2
-3
1
-4
0
-5
-30,000
-20,000
-10,000
0
10,000
20,000
30,000
Since the utility curve is slightly different from
a linear, therefore we can say that he is slightly
averse to risk.
Exercise 4-32
Solution:
μ1 = 18, μ2 = 21, σ1 = 7.4, σ2 = 8
Therefore we use combined estimate of mean
and standard deviation formula, we find:
μ = 19.41
σ = 7.67
So the distribution of no-shows is as follows:
19.41
Exercise 4-42
Solution:
Marginal profit = 200 – 20 = 180
Marginal loss = 90 – 60 = 30
Then
p(MP) = (1-p) (ML)
p (180) = (1-p) (30)
180p = 30 – 30p
210p = 30
Therefore
p = 0.143