Exam 6: Decision Making Under Uncertainty

The expected monetary value represents a long-run average.

Should the credit union purchase the report if it costs $150?

The solution procedure that was introduced in the book for decision trees is called the:

Why is there a kink in the line for the "Buy Insurance" line in the above strategy region chart?

Ms. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Ms. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder. Distribution of Accident Types and Corresponding Damage Amounts -Generate a statistical summary and risk profile for each of Mrs. Rich's possible decisions. Does this information impact her decision?

Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this prospect; the metallurgical properties of the ore and the net price (market price minus mining and transportation costs) of the ore in the future. The metallurgical properties of the ore would be classified as either "high grade" or "low grade". Southport's geologists have estimated that there is a 70% chance that the ore will be "high grade", and otherwise, it will be "low grade". Depending on the net price, both ore classifications could be commercially successful. The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport's economists have simplified the continuous distribution of possible prices into a two-outcome discrete distribution ("high" or "low" net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in millions of dollars), are summarized below. -Since the core test can only sample a small part of the mine, Southport's geologists believe it is somewhat unrealistic to view it as a perfectly reliable test. Based on similar tests they have conducted in the past, they believe that if the metallurgical properties of the ore are actually High Grade, then the probability that this test will return "favorable" results is 0.95. If the metallurgical properties are Low Grade, the probability that this test will return "favorable" results is only 0.25. Otherwise, the test results will be considered "unfavorable". Given this information, what are the posterior probabilities that the ore will be a High Grade and Low Grade, given the core test report?

Ms. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Ms. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder. Distribution of Accident Types and Corresponding Damage Amounts -Determine the payoffs associated with each possible decision and type of accident (cost in dollars).

Bayes' rule can be used for updating the probability of an uncertain outcome after observing the results of a test or study.

The following is a payoff table giving profits for various situations: States of Nature The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2 respectively. -What else might one consider in choosing from among these alternatives?

A risk profile from PrecisionTree lists:

Using a strategy region graph, determine what impact, if any, the insurance deductible amount has on her decision. Briefly explain your answer

The Waco Tire Company (WTC) is considering expanding production to meet possible increases in demand. WTC's alternatives are to construct a new plant, expand the existing plant, or do nothing in the short run. It will cost them $1 million to build a new facility and $600,000 to expand their existing facility. The market for this particular product may expand, remain stable, or contract. ETC's marketing department estimates the probabilities of these market outcomes as 0.30, 0.45, and 0.25, respectively. The expected revenue for each alternative is presented in the table below. -Generate a risk profile for each of WTC's possible decisions in this problem. Characterize the differences in risk for the different options.

In a single-stage decision problem, a single decision is made first, and then all uncertainty is resolved.

In decision trees, any branches leading into a node (from the left) have already occurred.

The expected value of sample information (EVSI) is the difference between the EMV we can obtain with sample information and the EMV we can obtain without information.

Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this prospect; the metallurgical properties of the ore and the net price (market price minus mining and transportation costs) of the ore in the future. The metallurgical properties of the ore would be classified as either "high grade" or "low grade". Southport's geologists have estimated that there is a 70% chance that the ore will be "high grade", and otherwise, it will be "low grade". Depending on the net price, both ore classifications could be commercially successful. The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport's economists have simplified the continuous distribution of possible prices into a two-outcome discrete distribution ("high" or "low" net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in millions of dollars), are summarized below. -Suppose that Southport could consider another alternative - postponing the go/no-go decision on the new venture and drilling for a core sample of the ore to determine with complete certainty its metallurgical property. How much should Southport be willing to pay for the core sample?

The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what type of program format to offer. She is considering three formats; rock, country, and rap. The number of listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends on the number of listeners the station has. Three broad categories of audience type can be described as A1, A2, and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and the rap music format draws mainly from the A3 listener. The station owner does not know which type of audience will dominate the community once its growth has stabilized. Probabilities have been assigned to the potential dominant audience, based on the community growth that has already occurred in this area. Since she wants to begin building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station owner has been able to construct the following payoff table, in which the entries are average monthly revenue in thousands of dollars. Audience -As the average monthly revenue associated with the rock format and an A1 audience varies between about $142,500 and $200,000, what happens to the maximum expected revenue? Briefly explain why.

What course of action is optimal for WTC? What is the expected profit in that case?

The expected value of perfect information (EVPI) is equal to:

Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this prospect; the metallurgical properties of the ore and the net price (market price minus mining and transportation costs) of the ore in the future. The metallurgical properties of the ore would be classified as either "high grade" or "low grade". Southport's geologists have estimated that there is a 70% chance that the ore will be "high grade", and otherwise, it will be "low grade". Depending on the net price, both ore classifications could be commercially successful. The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport's economists have simplified the continuous distribution of possible prices into a two-outcome discrete distribution ("high" or "low" net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in millions of dollars), are summarized below. -What should the Southport do? What is their expected profit?