For the following profit table: S1 S2 S3 S4 D1 50 75 20 30 D2 80 15 40 50 D3 -10
ID: 451985 • Letter: F
Question
For the following profit table:
S1
S2
S3
S4
D1
50
75
20
30
D2
80
15
40
50
D3
-100
300
-50
10
D4
25
25
25
25
Show your manual calculations for all of the following parts, no credit will be given otherwise:
1. What decision would be made under optimistic approach? under pessimistic approach?
2. What decision would be made under minimax regret?
3. What decision would be made under Laplace approach?
4. What decision would be made under criterion of realism? use = .75
5. If the probabilities of the states of nature are, respectively, .5, .35, .05, and .1 which decision would be chosen?
6. What is the expected value of perfect information?
S1
S2
S3
S4
D1
50
75
20
30
D2
80
15
40
50
D3
-100
300
-50
10
D4
25
25
25
25
Explanation / Answer
Payoff matrix 1.a) optimistic approach MaxiMax S1 S2 S3 S4 Max Payoff Maximin D1 50 75 20 30 75 D2 80 15 40 50 80 D3 -100 300 -50 10 300 300 Choose this one D4 25 25 25 25 25 1.b) Pessimistic approach Maxi min S1 S2 S3 S4 Min Payoff Maximin D1 50 75 20 30 20 D2 80 15 40 50 15 D3 -100 300 -50 10 -100 D4 25 25 25 25 25 25 Choose this one 2 Mini Max regret S1 S2 S3 S4 D1 50 75 20 30 D2 80 15 40 50 D3 -100 300 -50 10 D4 25 25 25 25 Regret Matrix S1 S2 S3 S4 Max regrets Min regret D1 30 225 20 20 225 D2 0 285 0 0 285 D3 180 0 90 40 180 180 Choose this one D4 55 275 15 25 275 3 laplace Matrix S1 S2 S3 S4 EMV D1 50 75 20 30 55.25 Choose this one D2 80 15 40 50 52.25 D3 -100 300 -50 10 53.5 D4 25 25 25 25 25 Given Probability 0.5 0.35 0.05 0.1 product =prob* element EMV EMV D1 25 26.25 1 3 55.25 EMV D2 40 5.25 2 5 52.25 EMV D3 -50 105 -2.5 1 53.5 EMV D4 12.5 8.75 1.25 2.5 25 4 Criterion of Realism S1 S2 S3 S4 Max Payoff Min Payoff EMV D1 50 75 20 30 75 20 61.25 D2 80 15 40 50 80 15 63.75 D3 -100 300 -50 10 300 -100 200 D4 25 25 25 25 25 25 25 Given alpha () 0.75 Expected Monetary value *M+(1-)m 5 Hurvitz S1 S2 S3 S4 Max Payoff Min Payoff EMV D1 50 75 20 30 75 20 61.25 D2 80 15 40 50 80 15 63.75 D3 -100 300 -50 10 300 -100 200 D4 25 25 25 25 25 25 25 Given alpha () 0.75 Expected Monetary value *M+(1-)m 6 expected value of perfect information S1 S2 S3 S4 EMV D1 50 75 20 30 55.25 expected value without perfect information(EV Without Payoff) D2 80 15 40 50 52.25 D3 -100 300 -50 10 53.5 D4 25 25 25 25 25 Given Probability 0.5 0.35 0.05 0.1 EV With PI 152 expected value of perfect information EVwith PI-Evwithout PI = 96.75
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