Exam 9: Decision Making Under Uncertainty

For each possible decision and each possible outcome,the payoff table lists the associated monetary value.

A spider chart shows both the range (as a percentage)of the variability of the input variables as well as the resulting changes in the expected value.

Probabilities on the branches of a chance node may be ____ events that have occurred earlier in the decision tree.

The sensitivity of the expected value to changes in the input variables can be inferred from a spider chart by observing:

Exhibit 9-2 A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate.If the credit union does not approve the loan application,the $20,000 will be invested in bonds that earn a 6% annual return.Without additional information,the credit union believes that there is a 5% chance that this customer will default on the loan,assuming that the loan is approved.If the customer defaults on the loan,the credit union will lose the $20,000. -Refer to Exhibit 9-2.The bank can thoroughly investigate the customer's credit record and obtain a favorable or unfavorable recommendation.If the credit report is perfectly reliable,what is the most the credit union should be willing to pay for the report?

Prior probabilities are sometimes called likelihoods,the probabilities that are influenced by information about the outcome of an earlier uncertainty.

Exhibit 9-1 A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing.If the temperature drops too low he runs the risk of losing his entire crop,valued at $75,000.Based on the National Weather Service,the probability of such a temperature drop is 60%.He can insulate his crop by spraying water on all the trees,which will cost $20,000.This action might succeed in protecting the crop,with the following possible outcomes: -Refer to Exhibit 9-1.Suppose that,in addition to the uncertainty about the probability of freezing,he is also uncertain about the cost of the insulation (could vary from $10,000 to $30,000).To which of these variables is the expected value most sensitive?

Exhibit 9-2 A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate.If the credit union does not approve the loan application,the $20,000 will be invested in bonds that earn a 6% annual return.Without additional information,the credit union believes that there is a 5% chance that this customer will default on the loan,assuming that the loan is approved.If the customer defaults on the loan,the credit union will lose the $20,000. -Refer to Exhibit 9-2.What should the credit union do? What is their expected profit?

Exhibit 9-1 A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing.If the temperature drops too low he runs the risk of losing his entire crop,valued at $75,000.Based on the National Weather Service,the probability of such a temperature drop is 60%.He can insulate his crop by spraying water on all the trees,which will cost $20,000.This action might succeed in protecting the crop,with the following possible outcomes: -Refer to Exhibit 9-1.Suppose the farmer is uncertain about the reliability of the National Weather Service forecast.If he thinks the probability of a freeze occurring could be anywhere between 40% and 80%,would that change his decision?

The expected value of sample information (EVSI)is the difference between the EMV obtained with sample information and the EMV obtained without any information.