Question

Consider the following Profit Payoff Table:

State of Nature |
|||

Decision Alternative |
S1 |
S2 |
S3 |

d1 |
250 |
100 |
25 |

d2 |
100 |
100 |
75 |

The probabilities for the states of nature are

P(S_{1}) = 0.65,

P(S_{2}) = 0.15, and

P(S_{3}) = 0.20.

- What is the optimal decision strategy if perfect information were available?
- What is the expected value for the decision strategy developed in part (a)?
- Using the expected value approach, what is the recommended decision without perfect information? What is its expected value?
- What is the expected value of perfect information?

Answer #1

Problem 13-14 (Algorithmic) The following profit payoff table
shows profit for a decision analysis problem with two decision
alternatives and three states of nature: State of Nature Decision
Alternative S1 S2 S3 d1 250 100 100 d2 200 100 150 The
probabilities for the states of nature are P(s1) = 0.45, P(s2) =
0.25 and P(s3) = 0.3. What is the optimal decision strategy if
perfect information were available? S1 : S2 : S3 : What is the
expected value...

The following payoff table shows a profit for a decision
analysis problem with two decision alternatives and three states of
nature. In order to get full credit, show your all work done step
by step including cell calculations using excel functions.
State of Nature
Decion Alternatives
s1
s2
s3
d1
250
100
50
d2
100
75
100
a) Construct a decision tree for this problem.
b) Suppose that the decision-maker obtains the probabilities
P(s1)=0.65, P(s2)=0.15, and P(s3)=0.20.
Use the expected...

State
of
Nature
Decision Alternative
s1
s2
s3
s4
d1
600
400
-100
120
d2
700
-200
0
400
d3
700
-200
0
400
P(si)
0.3
0.4
0.2
0.1
For a lottery having a payoff 700 with probability p and -200
with probability (1-p), the decision maker expressed the following
indifference probability. Suppose U (700) =100 and U (-200)
=-10.
Payoff
Indifferent Probability
600
0.95
400
0.8
120
0.5
0
0.35
-100
0.2
a) Complete the utility table by using...

Q.1 Payoff Table: Choices: D1, D2, D3. States of Nature: S1, S2,
S3. Profit( in millions) for each of the States of Nature are given
below: For D1: $100, $400, $500. For D2:-$100, $500, $900. For D3:
-$200, $500, $1600. P(s1)=0.4, P(s2)=0.4, P(s3)=0.2. Sample
Information Data: Market Research Firm provides following data:
conditional probabilities: P(Fav/s1)= 0.40, P(Fav/s2)= 0.5,
P(Fav/s3)= 0.9. Then P(Fav)= .54
For the data given in Q.1, compute revised probabilities, draw
the decision tree, and enter the payoff...

Consider a decision situation with four possible states of
nature: s1, s2,
s3, and s4. The prior
probabilities are P(s1) = 0.35,
P(s2) = 0.15,
P(s3) = 0.20,
P(s4) = 0.30. The conditional
probabilities are P(C|s1) =
0.2, P(C|s2) = 0.09,
P(C|s3) = 0.15, and
P(C|s4) = 0.20. Find the
revised (posterior) probabilities
P(s1|C),
P(s2|C),
P(s3|C), and
P(s4|C).

Problem 13-01 (Algorithmic) The following payoff table shows
profit for a decision analysis problem with two decision
alternatives and three states of nature: State of Nature Decision
Alternative S1 S2 S3 d1 260 140 100 d2 170 130 50 Choose the
correct decision tree for this problem. (i) d2d1s3s2s1s3s2s1 (ii)
d2d1s3s3s2s2s1s1 (iii) s3s2s1d2d1d2d1d2d1 (iv) d2d1s3s2s1s3s2s1 If
the decision maker knows nothing about the probabilities of the
three states of nature, what is the recommended decision using the
optimistic, conservative, and...

State of Nature
P
(Sj|I)
S1
S2
S3
Suppose that you are given a decision situation with three
possible states of nature: S1, S2, and S3. The prior probabilities
are P(S1) = 0.24, P(S2) = 0.60, and P(S3) = 0.16. With sample
information I, P(I | S1) = 0.10, P(I | S2) = 0.07, and P(I | S3) =
0.18. Compute the revised or posterior probabilities: P(S1 | I),
P(S2 | I), and P(S3 | I). If required, round your...

Problem 13-29 (Algorithmic) Three decision makers have assessed
utilities for the following decision problem (payoff in dollars):
State of Nature Decision Alternative S1 S2 S3 d1 30 50 -30 d2 80
110 -100 The indifference probabilities are as follows:
Indifference Probability (p) Payoff Decision maker A Decision maker
B Decision maker C 110 1.00 1.00 1.00 80 0.95 0.80 0.85 50 0.85
0.70 0.75 30 0.75 0.55 0.60 -30 0.60 0.25 0.50 -100 0.00 0.00 0.00
Find a recommended decision...

Suppose that you are given a decision situation with three
possible states of nature: S1, S2, and S3. The prior probabilities
are P(S1) = 0.21, P(S2) = 0.47, and P(S3) = 0.32. With sample
information I, P(I | S1) = 0.14, P(I | S2) = 0.06, and P(I | S3) =
0.20. Compute the revised or posterior probabilities: P(S1 | I),
P(S2 | I), and P(S3 | I). If required, round your answers to four
decimal places.

Consider the following payoff table that represents the
profits earned for each alternative (A, B, and C) under the states
of nature S1, S2, and S3.
S1 S2 S3
A $60 $145 $120
B $75 $125 $110
C $95 $85 $130
Refer to the payoff table. What is the expected value of
perfect information (EVPI)? Assume P(S1) = 0.5 and P(S2) = 0.25.
(Points : 2)

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