Problem 13-29 (Algorithmic)Three decision makers have assessed utilities for the following decision problem (payoff in dollars):100806030Decision Alternative S₁The indifference probabilities are as follows:-10-80did2Payoff Decision maker A1.000.950.850.750.600.00Indifference Probability (p)Decision maker AEU(01) -EU(42) =Recommended decision: di ✔Decision maker BEU(01) -EU(02) =Recommended decision: d2 ✔Decision maker CEU(d1) =State of NatureS₂EU(02) =Recommended decision: d2d2✔308060100Find a recommended decision for each of the three decision makers, if P(S1) = 0.25, P(S2)= 0.45, and P($3)= 0.30. (Note: For the same decision problem, different utilities can lead to different decisions.) If required, round your answers to two decimal places.Decision maker B1.000.800.700.550.250.00S₁-10-80Decision maker C1.000.85T0.750.600.500.00

Decision maker A: EU(d1) = 0.75EU(d2) = 0.6875 = 0.69 (Rounded to 2 decimal places) Recommended…

Answered: Problem 13-29 (Algorithmic) Three…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Questions 1, 2 and 3 are based on the following table. In the following table of costs, n1 and n2 are the states of nature, and a1, a2 and a3 are your decision alternatives: n1 n2a1 5 3a2 1 4a3 2 k Q.1. Suppose k = 6. If n1 occurs with probability p, If n1 occurs with probability p, for what values of p will a3 be the best decision alternative based on expected values, for what values of p will a1 be the best and for what values of p will a2 be the best? Q.2. Suppose n1 occurs with probability p. For what all values of k is a3 always better than a1 (based on expected values)? Q.3. What is the EVPI?
2
Group problems: The Collision Problem: You have been hired by an insurance investigator to look into an accident involving a sailboat and a speedboat that occurred on New Year's day at 3:00 in the arternoon. Your job is to determine where (relative to the dock) the collision took place. After your investigation you ascertain the following facts about the case. The speedboat was carrying a toup of 20 people who were returning to shore after enjoying a 2-hour picnic on an island. The island is located 5.2 miles east and 12.6 miles north of the dock. The speedboat was heading from the island toward a point on the shore located 3.0 miles due west of the dock. Around the same time, the sailboat left the dock heading toward a buoy that is 5.0 miles west and 7.5 miles north of the dock. Neither boat made it to its destination since they collided in the water. You interviewed 5 witnesses and 2 lifeguards for 4 hours, in addition to studying nautical maps provided by the Navy. You plan to bill…
The following profit payoff table was presented in Problem 1: State of Nature Decision Alternative d, d, 250 100 25 100 100 75 The probabilities for the states of nature are P(sj) = 0.65, P(s2) = 0.15, and P(s3) = 0.20. a. What is the optimal decision strategy if perfect information were available? b. What is the expected value for the decision strategy developed in part (a)? c. Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? d. What is the expected value of perfect information?
(Problem Set #8) A new soft drink is being market tested. A sample of 120 individuals participated in the taste test and 36 indicated that they like the taste. We are interested in determining if more than 25% of the consumers will like the new soft drink. Let p = the proportion of all consumers who like the new soft drink. The p-value of the test is O a. less than 0.01 b. 0.0031 O c. 0.0122 d. 0.1038
27. An enquiry into the budgetk of the middle class families in Mumbai gave the following information : Fuel 10% Misc. 20%· Еxpenditure Price (2002) Rs. Price (2003) Rs. Food 35% Rent 15% Clothing 20% 100 20 60 150 50 174 60 125 25 90 The cost of living index in 2003 is : (A) 116.10 (В) 126.10 (C) 136.10 (D) 146.10.
Refer to the contingency table shown below. Smoking by Race for Males Aged 18 to 24 Smoker(S) Nonsmoker(N) Row Total White(W) 290 560 850 Black(B) 30 120 150 Column Total 320 680 1,000 Click here for the Excel Data File (a) Calculate the probabilities given below (Round your answers to 4 decimal places.): Smoking by Race for Males Age 18-24 Smoker Nonsmoker Row Total (S) (N) White (W) 290 560 850 Black (B) 30 120 150 Column Total 320 680 1000 Smoking by Race for Males Age 18-24 Smoker Nonsmoker Row Total (S) (N) White (W) 290 560 850 Black (B) 30 120 150 Column Total 320 680 1000
The accompanying data came from a study of collusion in bidding within the construction industry. No. Bidders No. Contracts 2 3 4 5 6 7 8 9 10 11 USE SALT 8 20 26 18 12 8 6 7 4 3 (a) What proportion of the contracts involved at most five bidders? At least five bidders? (Round your answers to four decimal places.) at most five bidders. at least five bidders X X (b) What proportion of the contracts involved between five and 10 bidders, inclusive? Strictly between five and 10 bidders? (Round your answers to four decimal places.) between five and 10 bidders, inclusive strictly between five and 10 bidders X X
A payoff table is given as S1 S2 S3 D1 250 750 500 D2 300 -250 1200 D3 500 500 600 a. What choice should be made by the optimistic decision maker? b. What choice should be made by the conservative decision maker? c. What decision should be made under minimax regret? d. If the probabilities of d1, d2, and d3 are .2, .5, and .3 respectively, then what choice should be made under expected value?
A decision maker faced with four decision altematives and four states of nature develops the following profit payoff table. States of Nature Decision Alternative s. 52 5 5. d. 12 7 3 5 d, 7 d. 6 8 9 11 The decision maker obtains information that enables the following probabilities assessments: P(s,) = 0.5, P(s,) = 0.2, P(s,) = 0.2, and P(s,) = 0.1. (a) Use the expected value approach to determine the optimal decision. EV(d,) EV(d,) EV(d,) EV(d.) The optimal decision is (b) Now assume that the entries in the payoff table are costs. Use the expected value approach to determine the optimal decision. The optimal decision is ? v in
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A company is facing three types of decisions for the purchasing of a seasonal product. The profitprojection may depend on the demand level. The payoffs for the situations are given in the followingtable:DemandDecision High (s1) Medium (s2) Low (s3)d1 60 60 50d2 80 80 30d3 100 70 101. If the prior probabilities are 0.3, 0.3, and 0.4, respectively, what is the recommended decision?Show all the calculations and answer with a decision tree.2. At each preseason sales meeting, the vice president of sales provides a personal opinion regarding potential demand for the product. The prediction of the vice president have alwaysbeen either excellent (E) or very good (G). Posterior probabilities are as follows.P(V)=0.7; P(E)=0.3P(s1|E)=0.34; P(s1|V)=0.2P(s2|E)=0.32; P(s2|V)=0.26;Use a decision tree to give the optimal decision strategy.43. Give the EVPI and the EOL, and EVSI.4. Suppose that the prior probability of a low demand is always fixed to 0.4, give a sensitivityanalysis on the other…

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