Exam 6: Decision Making Under Uncertainty

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

A risk profile is a chart that represents the probability distribution of monetary outcomes for any decisions.

Decision trees are composed of nodes (circles,squares,and triangles)and branches (lines).

In decision trees,time proceeds from

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

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.

The Excel add-in,PrecisionTree,enables you to draw and label a decision tree.

Construct a decision tree to help the station identify its optimal format.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.

In decision trees,a probability node (a circle)is a time when the decision maker makes a decision.

In a multistage decision problem,decisions and outcomes alternate.That is,a decision maker makes a decision,then some uncertainty is resolved,then the decision maker makes a second decision,then some further uncertainty is resolved,and so on.

Bayes' is useful in determining the value of perfect information (EVPI).

With regard to decision making,most individuals are _____.

A strategy region graph is useful for seeing whether the decision changes over the range of the input variable.

The certainty equivalent is the certain dollar amount a risk-averse decision maker would accept in order to avoid a gamble altogether.

The expected value of perfect information (EVPI)is the difference between the EMV with perfect information and the EMV with no additional information.

In general,the expected monetary values (EMV)represent possible payoffs.

The decision maker now has $10,000 and two possible decisions.For Alternative 1,she loses $500 for certain (x=$9,500).For Alternative 2,she loses $0 (x=$10,000)with probability 0.9 and loses $5,000 (x=$5,000)with probability 0.10.Which alternative maximizes the expected utility of her net wealth?

Suppose that an actual (not perfectly reliable)market research report has the following characteristics based on historical data: if the program is actually going to be a hit,there is a 90% chance that the market researchers will predict the program to be a hit,and if the program is actually going to be a flop,there is a 20% chance that the market researchers will predict the program to be a hit.Given this information,what are the posterior probabilities that a show will be a hit or a flop,given the market research report?

A risk profile lists the full probability distribution.

Because 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?