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Exam 20: Decision Analysis

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Question 21

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You are given the following payoff table: Assume the following probability information is given: a.Find the values of P(I₁) and P(I₂). b.What are the values of P(S₁ | I₁), P(S₂ | I₁), P(S₁ | I₂), and P(S₂ | I₂)? c.Use the decision tree approach and determine the optimal decision strategy. What is the expected value of the solution? d.Determine the expected value of sample information.

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a.0.41, 0.59
b.0.658...

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Question 22

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Exhibit 20-1 Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of occurrence of S₁ = 0.2. -Refer to Exhibit 20-1. The recommended decision alternative based on the expected value is

A) A
B) B
C) C
D) All alternatives are the same.

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Question 23

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Assume you are faced with the following decision alternatives and two states of nature. The payoff table is shown below. Assume the states of nature have the following probabilities: P(S₁) = 0.4, P(S₂) = 0.6 a.Determine the expected value of each alternative and indicate which decision alternative is the best. b.Determine the expected value of perfect information.

A sequence of decisions and chance outcomes that provide the optimal solution to a decision problem is called

Exhibit 20-5 Below you are given a payoff table involving three states of nature and three decision alternatives. The probability of occurrence of S₁ is 0.2 and the probability of occurrence of S₂ is 0.3. -Refer to Exhibit 20-5. The recommended decision alternative based on the expected value is

New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is

Exhibit 20-3 Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of the occurrence of state of nature S₁ is 0.4. -Refer to Exhibit 20-3. The expected value of perfect information equals

Exhibit 20-2 Below you are given a payoff table involving three states of nature and two decision alternatives. The probability that S₁ will occur is 0.1; the probability that S₂ will occur is 0.6; and the probability that S₃ will occur is 0.3. -Refer to Exhibit 20-2. The expected value of perfect information equals

You are given a decision situation with three possible states of nature S₁, S₂, and S₃. The prior probabilities of the three states are 0.20, 0.45, and 0.35. With sample information I, you are provided with the following information. a.Compute P(I). b.Compute the revised probabilities of P(S₁|I), P(S₂|I), and P(S₃|I).

The probability of the states of nature, after use of Bayes' theorem to adjust the prior probabilities based upon given indicator information, is called

Exhibit 20-3 Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of the occurrence of state of nature S₁ is 0.4. -Refer to Exhibit 20-3. The recommended decision based on the expected value criterion is

Suppose we are interested in investing in one of three investment opportunities: d₁, d₂, or d₃. The following profit payoff table shows the profits (in thousands of dollars) under each of the 3 possible economic conditions: S_l, S₂, and S₃. The probability of the occurrence of S₁ is 0.1, and the probability of the occurrence of S₂ is 0.3. a.Determine the expected value of each alternative and indicate which decision alternative is the best. b.Determine the expected value with perfect information about the states of nature. c.Determine the expected value of perfect information.

Below you are given a payoff table involving two states of nature and two decision alternatives. The probability of the occurrence of S₁ is 0.3. a.Compute the expected value for each decision. Which decision is the best? b.Compute the expected value of perfect information.

A group of investors wants to open up a jewelry store in a new shopping center. The investors are trying to decide whether to stock the store with inexpensive jewelry, medium-priced jewelry, or expensive jewelry. The probability of their choice depends upon the economic conditions. The payoff table below gives the anticipated profits for different states of the economy. The probability of prosperity is 0.5. a.Determine the expected value of each alternative and indicate which decision alternative is the best. b.Determine the expected value with perfect information about the states of nature. c.Determine the expected value of perfect information.

An investor has a choice between four investments. The profitability of the investments depends upon the market. The payoff table is given below for different market conditions. a.A market economist has stated that there is a 25% chance that the market will stay the same, a 35% chance that the market will decrease, and a 40% chance that the market will increase. Compute the expected value for each investment. Which investment is the best? b.Compute the expected value of perfect information.

The probabilities of states of nature after revising the prior probabilities based on given indicator information are

Shannon Lipscomb & Associates (SLA) are producers of a new brand of personal computers. SLA is considering employing a market research firm to supply indicator information related to the demand for their computers. The information would consist of forecasts of light demand (I₁) or heavy demand (I₂) for SLA's computers. The following conditional probabilities reflect the accuracy of the market research firm's forecasts: a.Compute the posterior probabilities. b.What decision should be taken if the market research firm forecasts light demand (I₁)? Heavy demand (I₂)? c.Calculate the expected value of sample information. d.Compute the expected value of perfect information.

An intersection or junction point of a decision tree is called a (n)

The difference between the expected value of an optimal strategy based on sample information and the "best" expected value without any sample information is called the

Suppose we are interested in investing in one of three investment opportunities: d₁, d₂, or d₃. The following profit payoff table shows the profits (in thousands of dollars) under each of the 3 possible economic conditions-S₁, S₂, and S₃: Assume the states of nature have the following probabilities of occurrence: P(S₁) = 0.2 P(S₂) = 0.3 P(S₃) = 0.5 a.Determine the expected value of each alternative and indicate which decision alternative is the best. b.Determine the expected value with perfect information about the states of nature. c.Determine the expected value of perfect information.