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# Predict the expected value of perfect information.

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4. Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new dealership. They have three offers: from a foreign compact car company, from a U.S. - producer of full-sized cars, and from a truck company. The success of each type of dealership will depend on how much gasoline is going to be available during the next few years. The profit from each type of dealership, given the availability of gas, is shown in the following payoff table:

Gasoline Availability

Dealership Shortage Surplus

.6 .4

______________________________________________________

Compact cars \$300,000 \$150,000

Full-sized cars 100,000 600,000

Trucks 120,000 170,000

a. Determine which type of dealership the couple should purchase using the expected value criterion.

b. Determine the expected value of perfect information.

https://brainmass.com/statistics/central-tendency/predict-the-expected-value-of-perfect-information-395163

#### Solution Summary

This solution explains the type of dealership the couple should purchase using the expected value criterion.

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## Probability Model; Decision Maker is Risk Neutral; Test Results

See attached file.

A decision maker is faced with the problem shown. Assume that the decision maker is risk neutral.

a) A test is available that will provide information about the possible outcomes associated with A. Add a branch called 'do the test' to the decisions below. Show how the test can be used to guide the selection of A or B. Previous evaluations of the test's performance indicate that when the outcome was 'good' the test indicated 'good' 90% of the time. Given that the outcome was 'bad', the test predicted 'bad' 40% of the time. What is the value of the information in the test? What is the optimal strategy for the decision maker to follow?

b) Suppose the test results in the past show that the test predicted 'good' 50% of the time when the outcome was 'good' and predicted 'bad' 50% of the time when the outcome was 'bad'. What is now the value of the information in the test? Why? What is the optimal strategy when this test is used?

c) What is the value of perfect information about outcome A?

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