Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
6th Edition
ISBN: 9781337115186
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
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Chapter 20.4, Problem 15E
In the following profit payoff table for a decision problem with two states of nature and three decision alternatives, the prior probabilities for s1 and s2 are P(s1) = .8 and P(s2) = .2.
| State of Nature | ||
| Decision Alternative | s1 | s2 |
| d1 | 15 | 10 |
| d2 | 10 | 12 |
| d3 | 8 | 20 |
- a. What is the optimal decision?
- b. Find the EVPI.
- c. Suppose that sample information I is obtained, with P(I | s1) = .20 and P(I | s2) = .75. Find the posterior probabilities P(s1 | I) and P(s2 | I). Recommend a decision alternative based on these probabilities.
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The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.
DecisionAlternative
States of Nature
s1
s2
s3
d1
240
90
15
d2
90
90
65
Suppose that the decision maker obtained the probabilities
P(s1) = 0.65, P(s2) = 0.15,
and
P(s3) = 0.20.
Use the expected value approach to determine the optimal decision.
EV(d1) =
EV(d2) =
The optimal decision is ?
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
250
100 25
d2
100
100 75
1) Construct a decision tree for this problem.
2) 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 minimax regret approaches?
Consider the following profit payoff table.
The prior probabilities for s1 and s2 are P(s1)=0.8 and P(s2)=0.2.
States of Nature
Decision Alternative
s1
s2
d1
15
10
d2
10
12
d3
8
20
a. What is the optimal decision?
b. Find the EVPI.
c. Suppose that sample information I is obtained, with P(I|s1)=0.20 and P(I|s2)=0.75. Find the posterior probabilities P(s1|I) and P(s2|I). Recommend a decision alternative based on these probabilities.
Chapter 20 Solutions
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
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