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
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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.
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- Consider the following profit payoff table and probability assessments: States of Nature Decision Alternative s1 s2 s3 s4 d1 14 9 10 5 P(s1)= 0.5 d2 11 10 8 7 P(s2)= 0.2 d3 9 10 10 11 P(s3)= 0.2 d4 8 10 11 13 P(s4)= 0.1 a. Use the expected value approach to determine the optimal solution. b. If the entries in the payoff table are costs, determine the optimal decision using the expected value approach.For the following payoff table, the probability of event 1 is 0.8, the probability of event 2 is 0.1, and the probability of event 3 is 0.1 ACTION ACTION EVENT A ($) B ($) 1 50 10 2 300 100 3 500 200 a. Determine the optimal action based on the maximax criterion b. Determine the optimal action based on the maximin criterion c. Explain the meaning of the Expected Value of Perfect Information (EVPI) in this problemAnita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go") so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that of its customers order their food to go. Suppose that this proportion is correct and that a random sample of individual customers is taken. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of customers in the sample who order their food to go by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.
- You and two other people are to place bids for an object, with the high bid winning. If you win, you plan to sell the object immediately for 10,000.(a) How much should you bid to maximize your expected profit if you believe that the bids of the others can be regarded as being independent and uniformly distributed between 7,000 and 10,000?Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go") so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that 45% of its customers order their food to go. Suppose that this proportion is correct and that a random sample of 50 individual customers is taken. Answer the following. (a) Estimate the number of customers in the sample who order their food to go by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.For the following payoff table, the probability of event 1 is 0.8, the probability of event 2 is 0.1, and the probability of event 3 is 0.1 ACTION ACTION EVENT A ($) B ($) 1 50 10 2 300 100 3 500 200 a. Determine the optimal action based on the maximax criterion b. Compute the Expected Monetary Value (EMV) for action A c. Explain the meaning of the Expected Value of Perfect Information (EVPI) in this problem
- Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go") so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that 48% of its customers order their food to go. Suppose that this proportion is correct and that a random sample of 50 individual customers is taken. A) Estimate the number of customers in the sample who order their food to go by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. B) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal placesThe Navy uses a certain type of vacuum tube in a sonar scanning device. Based on past experience, the vacuum tube exhibits the following failure pattern: Number of Months of Operation Probability of Failure1 0.12 0.13 0.24 0.15 0.36 0.2 Failures during operation cost $200 each, but the tube can be replaced before failure for $50. Find the optimal replacement strategy.Derive the conditional likelihood under m:1 matching where the model includes only treatment as a covariate.
- You and two other people are to place bids for an object, with the high bid winning. If you win, you plan to sell the object immediately for 10,000.(a) How much should you bid to maximize your expected profit if you believe that the bids of the others can be regarded as being independent and uniformly distributed between 7,000 and 10,000?(b) How much should you bid to maximize your expected profit if you believe that the bids of the others can be regarded as identical and uniformly distributed between 7,000 and 10,000?Hemmingway, Inc., is considering a $5 million research and development (R&D) project. Profit projections appear promising, but Hemmingway's president is concerned because the probability that the R&D project will be successful is only 0.50. Furthermore, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $20 million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized. Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated $25 million. Under this option, the company would not build the $20 million production facility. The decision tree is shown in Figure 4.16. The profit projection for each outcome is shown at the end of the branches. For example, the revenue projection for the high demand outcome is $59 million.…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?
