Exam 18: Decision Theory

A corn farmer has categorized the weather into three possible levels.The weather conditions will affect the timing of the harvest and the associated payoff.In this situation,the weather conditions are called the ____________________.

The maximax criterion finds the best possible payoff for each alternative and then chooses the alternative that yields the maximum (best)possible payoff.

The quality control manager for NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)an incoming shipment (lot)of microchips.The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁),50 percent chance that the lot is fair quality (S₂),and 20 percent chance that the lot is good quality (S₃).Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. Based on historical data,if the lot is poor quality,40 percent of the items are defective.If the lot is fair quality,22 percent of the items are defective.If the lot is good quality,10 percent of the items are defective.The quality control manager inspects one unit from a recent shipment.After inspecting it,he determines that the unit is defective.Based on this additional information,determine the revised (posterior)probabilities for each of the three states of nature.

Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (S_I)represent the levels of demand for the company products.S₁,S₂,and S₃ characterize high,medium,and low demand,respectively.The payoff values are in thousands of dollars. The management believes that weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 15 months with high demand,28 months with medium demand,and 5 months with low demand.12 of the 15 months with high demand had favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.Construct the revised probability table for poor weather conditions,and find the probability of high demand given that the weather conditions are poor.

An automobile insurance company is in the process of reviewing its policies.The company is considering increasing the premium charged to drivers under 25.According to company records,35 percent of the insured drivers are under the age of 25.Company records also show that 280 of the 700 insured drivers under the age of 25 have been involved in at least one automobile accident.On the other hand,only 130 of the 1300 insured drivers 25 years or older have been involved in at least one automobile accident.An accident has just been reported.What is the probability that the insured driver is under the age of 25?

Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (S_I)represent the levels of demand for the company products.S₁,S₂,and S₃ characterize high,medium,and low demand,respectively.The payoff values are in thousands of dollars. The management believes that weather conditions significantly affect the level of demand.48 monthly sales reports are randomly selected.These monthly sales reports show 15 months with high demand,28 months with medium demand,and 5 months with low demand.12 of the 15 months with high demand had favorable weather conditions.14 of the 28 months with medium demand had favorable weather conditions.Only 1 of the 5 months with low demand had favorable weather conditions.Based on this information,the prior probabilities have been revised.If the weather conditions are favorable,P(S₁)= .4286,P(S₂)= .5357,and P(S₃)= .0357;and if the weather conditions are poor,P(S₁)= .1364,P(S₂)= .6818,and P(S₃)= .1818.It is also determined that the probability of favorable weather is 0.56 and the probability of poor weather is 0.44.Carry out a preposterior analysis and,using the revised probabilities,determine (1)the expected monetary value when the weather conditions are favorable and (2)the expected monetary value when the weather conditions are poor.

When we use the expected monetary value criterion,the expected payoff equals the actual payoff that will be realized.

The alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (S_I)represent the levels of demand for the company products.s₁,s₂,and s₃ characterize high,medium,and low demand,respectively.The payoff values are in thousands of dollars.Prior probabilities are .3 for s₁;.6 for s₂,and .1 for s₃. Find the expected monetary value for each of the alternatives and determine the best alternative (course of action)for the EKA manufacturing company using the expected monetary value criterion.

Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (S_I)represent the levels of demand for the company products.S₁,S₂,and S₃ characterize high,medium,and low demand,respectively.The payoff values are in thousands of dollars. The best alternative (course of action)for the EKA manufacturing company,using the maximax criterion,is alternative 1.

The quality control manager for NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)an incoming shipment (lot)of microchips.The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁),50 percent chance that the lot is fair quality (S₂),and 20 percent chance that the lot is good quality (S₃).Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. What is the maximum amount that the quality control manager would be willing to pay for perfect information?

When we assess the worth of sample information in a decision-making problem,we are performing a

The expected monetary value criterion is best used when a large number of similar decisions will be made.

The _______________________is the difference between the expected payoff of sampling and the expected payoff based on expected monetary criterion and prior probabilities.

Alternatives 1 and 2 in the following payoff table represent the two possible manufacturing strategies that the EKA manufacturing company can adopt.The level of demand affects the success of both strategies.The states of nature (S_i)represent the levels of demand for the company products.S₁,S₂,and S₃ characterize high,medium,and low demand,respectively.The payoff values are in thousands of dollars. The best alternative (course of action)for the EKA manufacturing company using the maximin criterion is strategy _____ and the best possible payoff is __________.

The _____________________ criterion is attractive to those decision makers who exhibit a neutral approach toward decision choices involving risk.

The _________ curve of an individual decision maker is a plot of their utilities versus the profits.

The quality control manager for NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)an incoming shipment (lot)of microchips.The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁),50 percent chance that the lot is fair quality (S₂),and 20 percent chance that the lot is good quality (S₃).Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. Based on historical data,if the lot is poor quality,40 percent of the items are defective.If the lot is fair quality,22 percent of the items are defective.If the lot is good quality,10 percent of the items are defective.The quality control manager inspects one unit from a recent shipment.After inspecting it,he determines that the unit is not defective.Given that the inspected item is not defective,determine which alternative action the quality control manager should choose.

The ______________ is the difference between the expected payoff that would be realized if the best alternative action were selected if we knew which state of nature would occur and the expected payoff under risk.

When making a decision in an environment of ________________,the decision maker knows which of the states of nature will actually occur.

Maximin is a criterion used when making decisions under _____________.