Exam 21: Decision Analysis

The owner of a new gourmet kitchenware shop wishes to determine how many days and evenings to keep the shop open.The various payoffs (in $1,000s)are indicated in the table below. Assume the probabilities of the three states of nature are P(S₁)= 0.60,P(S₂)=0 .30,and P(S₃)= 0.1. 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.

The Video Game Supply Company (VGS)is deciding whether to set production next year at 2,000,2,500,or 3,000 games.Demand could be low,medium,or high.Using historical data,VGS estimates the probabilities as 0.4 for low demand,0.3 for medium demand,and 0.3 for high demand.The following profit payoff table (in $100s)has been developed. a.Determine the expected value of each alternative and indicate what should be the production target. b.Determine the expected value with perfect information about the states of nature. c.Determine the expected value of perfect information.

Michael,Nancy,& Associates (MNA)produce color printers.The demand for their printers could be light,medium,or high with the following probabilities. The company has three production alternatives for the coming period.The payoffs (in millions of dollars)associated with the three alternatives are shown below. a.Compute the expected value of the three alternatives.Which alternative would you select,based on the expected values? b.Compute the expected value with perfect information (i.e. ,expected value under certainty). c.Compute the expected value of perfect information (EVPI).

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 monetary value for each decision.Which decision is the best? b.Compute the expected value of perfect information.

Assume you are faced with the following decision alternatives and two states of nature.The payoff table is shown below. The probability of state of nature 1 is P(s₁)= 0.42. a.Determine the expected value of each alternative. b.Which decision is the optimal decision? c.Determine the expected value with perfect information. d.Compute the expected value of perfect information.

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

The following payoff table shows profits for two decision alternatives under three different states of nature.It is known that the probability of the occurrence of state of nature 1 is 0.1. a.What should the probabilities of states of natures 2 and 3 be so that the expected values of the two decision alternatives equal one another? b.Determine the expected values.

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.

Exhibit 21-4 Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of the occurrence of S₁ = 0.3. -Refer to Exhibit 21-4.The expected value of the best alternative is

A decision criterion which weights the payoff for each decision by its probability of occurrence is known as the

For a decision alternative,the weighted average of the payoffs is known as

Information about a state of nature is known as

The probability of one event given the known outcome of a (possibly)related event is known as

Exhibit 21-3 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 21-3.The recommended decision based on the expected monetary value criterion is

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.

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

Exhibit 21-1 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 21-1.The expected value of perfect information is

Exhibit 21-5 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 21-5.The expected value of perfect information is

Exhibit 21-5 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 21-5.The expected monetary value of alternative C is

A poll released this week found that in a random sample of registered voters,60% indicated that they think a female "will run" for the presidency,30% said a female "will not run," and 10% had "no opinion." When asked their opinions on whether or not a female would be elected,66% of those who said a female "will run" thought she could be elected;25% of those who thought a female "will not run" thought she could be elected;whereas,20% of those who had no opinion said that she could be elected. a.What percentage of registered voters (in this sample)thought that a female could be elected? b.Given that a person thought that a female could be elected,what is the probability that this person said a female "will not run" for the presidency? c.Compute all the posterior probabilities.