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9.3e

Purchase Price $3
Selling Price $8
Payoff Table State of Nature
Sell Sell Sell Sell Expected
Alternative 10 11 12 13 Payoff
Buy 10 $50 $50 $50 $50 $50.00
Buy 11 $47 $55 $55 $55 $53.40
Buy 12 $44 $52 $60 $60 $53.60
Buy 13 $41 $49 $57 $65 $51.40
Prior Probability 0.2 0.4 0.3 0.1

9.3f (i)

Purchase Price $3
Selling Price $8
Payoff Table State of Nature
Sell Sell Sell Sell Expected
Alternative 10 11 12 13 Payoff
Buy 10 $50 $50 $50 $50 $50.00
Buy 11 $47 $55 $55 $55 $53.40
Buy 12 $44 $52 $60 $60 $55.20
Buy 13 $41 $49 $57 $65 $53.00
Prior Probability 0.2 0.2 0.5 0.1

9.3f (ii)

Purchase Price $3
Selling Price $8
Payoff Table State of Nature
Sell Sell Sell Sell Expected
Alternative 10 11 12 13 Payoff
Buy 10 $50 $50 $50 $50 $50.00
Buy 11 $47 $55 $55 $55 $53.40
Buy 12 $44 $52 $60 $60 $54.40
Buy 13 $41 $49 $57 $65 $52.20
Prior Probability 0.2 0.3 0.4 0.1

9.3f (iii)

Purchase Price $3
Selling Price $8
Payoff Table State of Nature
Sell Sell Sell Sell Expected
Alternative 10 11 12 13 Payoff
Buy 10 $50 $50 $50 $50 $50.00
Buy 11 $47 $55 $55 $55 $53.40
Buy 12 $44 $52 $60 $60 $52.80
Buy 13 $41 $49 $57 $65 $50.60
Prior Probability 0.2 0.5 0.2 0.1

9.7d

Payoff Table ($thousand) Expected
State of Nature Payoff
Alternative S1 S2 ($thousand)
A1 80 25 47
A2 30 50 42
A3 60 40 48
Prior Probability 0.4 0.6

9.7e

40%
State 1
80
Alternative 1 80 80
0 47 60%
State 2
25
25 25
40%
State 1
30
Alternative 2 30 30
3
48 0 42 60%
State 2
50
50 50
40%
State 1
60
Alternative 3 60 60
0 48 60%
State 2
40
40 40

9.7f (0.2)

20%
State 1 Payoff Table ($thousand)
80 State of Nature
Alternative 1 80 80 Alternative S1 S2
A1 80 25
0 36 80% A2 30 50
State 2 A3 60 40
25
25 25 Prior Probability 0.2 0.8
20% Best Alternative 2
State 1
30 Expected Payoff 46
Alternative 2 30 30 ($thousand)
2
46 0 46 80%
State 2
50
50 50
20%
State 1
60
Alternative 3 60 60
0 44 80%
State 2
40
40 40

9.7f (0.6)

60%
State 1 Payoff Table ($thousand)
80 State of Nature
Alternative 1 80 80 Alternative S1 S2
A1 80 25
0 58 40% A2 30 50
State 2 A3 60 40
25
25 25 Prior Probability 0.6 0.4
60% Best Alternative 1
State 1
30 Expected Payoff 58
Alternative 2 30 30 ($thousand)
1
58 0 38 40%
State 2
50
50 50
60%
State 1
60
Alternative 3 60 60
0 52 40%
State 2
40
40 40

9.7g

60%
State 1 Payoff Table ($thousand)
80 State of Nature
Alternative 1 80 80 Alternative S1 S2
A1 80 25
0 58 40% A2 30 50
State 2 A3 60 40
25
25 25 Prior Probability 0.6 0.4
60% Best Alternative 1
State 1
30 Expected Payoff 58
Alternative 2 30 30 ($thousand)
1
58 0 38 40%
State 2 Prior Expected
50 Probability Best Payoff
50 50 of S1 Alternative ($thousand)
1 58
60% 0.20 2 46
State 1 0.24 2 45.2
60 0.28 3 45.6
Alternative 3 60 60 0.32 3 46.4
0.36 3 47.2
0 52 40% 0.40 3 48
State 2 0.44 1 49.2
40 0.48 1 51.4
40 40 0.52 1 53.6
0.56 1 55.8
0.60 1 58

9.19b

Payoff Table ($millions) Expected
State of Nature Payoff
Alternative Successful Unsuccessful ($millions)
Develop Product 1.5 -1.8 0.4
Don't Develop Product 0 0 0
Prior Probability 0.667 0.333

9.19d

Template for Posterior Probabilities
Data: P(Finding | State)
State of Prior Finding
Nature Probability Predict Successful Predict Unsuccessful
Successful 0.667 0.8 0.2
Unsuccessful 0.333 0.3 0.7
Posterior P(State | Finding)
Probabilities: State of Nature
Finding P(Finding) Successful Unsuccessful
Predict Successful 0.633 0.842 0.158
Predict Unsuccessful 0.367 0.364 0.636

9.19e

84%
Successful
1.4
Develop Product 1.5 1.4
0 0.879 16%
63% Unsuccessful
Predict Success -1.9
1 -1.8 -1.9
0 0.879
Don't Develop
-0.1
0 -0.1
Conduct Survey
36%
-0.1 0.5200000004 Successful
1.4
Develop Product 1.5 1.4
0 -0.6999999995 64%
37% Unsuccessful
Predict Unsuccessful -1.9
2 -1.8 -1.9
0 -0.1
1 Don't Develop
0.5200000004 -0.1
0 -0.1
67%
Successful
1.5
Develop Product 1.5 1.5
0 0.4 33%
Unsuccessful
No Survey -1.8
1 -1.8 -1.8
0 0.4
Don't Develop
0
0 0

9.20b

Payoff Table State of Nature Expected
Alternative p = 0.05 p = 0.25 Payoff
Screen -$1,500 -$1,500 -$1,500
Don't Screen -$750 -$3,750 -$1,350
Prior Probability 0.8 0.2

9.20d

Template for Posterior Probabilities
Data: P(Finding | State)
State of Prior Finding
Nature Probability Defective Nondefective
p = 0.05 0.8 0.05 0.95
p = 0.25 0.2 0.25 0.75
Posterior P(State | Finding)
Probabilities: State of Nature
Finding P(Finding) p = 0.05 p = 0.25
Defective 0.09 0.444 0.556
Nondefective 0.91 0.835 0.165

9.20e

44.4%
p=0.05
-1625
Screen -1500 -1625
0 -1625 55.6%
p=0.25
9% -1625
Defective -1500 -1625
1
0 -1625 44.4%
p=0.05
-875
Don't Screen -750 -875
0 -2541.6666666667 55.6%
p=0.25
-3875
Pre-screen -3750 -3875
-125 -1392.95 83.5%
p=0.05
-1625
Screen -1500 -1625
0 -1625 16.5%
p=0.25
91% -1625
Nondefective -1500 -1625
2
0 -1370 83.5%
p=0.05
-875
Don't Screen -750 -875
2
-1350 0 -1370 16.5%
p=0.25
-3875
-3750 -3875
80%
p=0.05
-1500
Screen -1500 -1500
0 -1500 20%
p=0.25
-1500
Don't Pre-screen -1500 -1500
2
0 -1350 80%
p=0.05
-750
Don't Screen -750 -750
0 -1350 20%
p=0.25
-3750
-3750 -3750

9.27

70%
Growth
144
Stocks Y2 24 144
0 133.2 30%
Recession
70% 108
Growth -12 108
1
20 133.2 70%
Growth
126
Bonds Y2 6 126
0 127.8 30%
Recession
132
12 132
Stocks Y1 20%
Growth
100 122.94 108
18 108
70%
Stocks Y2 Recession
81
0 82.8 -9 81
10%
Depression
30% 45
Recession -45 45
2
-10 99 20%
Growth
94.5
4.5 94.5
70%
Bonds Y2 Recession
99
0 99 9 99
10%
1 Depression
122.94 108
18 108
70%
Growth
126
Stocks Y2 21 126
0 116.55 30%
Recession
70% 94.5
Growth -10.5 94.5
1
5 116.55 70%
Growth
110.25
Bonds Y2 5.25 110.25
0 111.825 30%
Recession
115.5
10.5 115.5
Bonds Y1 20%
Growth
100 117.885 132
22 132
70%
Stocks Y2 Recession
99
0 101.2 -11 99
10%
Depression
30% 55
Recession -55 55
2
10 121 20%
Growth
115.5
5.5 115.5
70%
Bonds Y2 Recession
121
0 121 11 121
10%
Depression
132
22 132