Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

Probabilities on the branches of a chance node are conditional probabilities because they depend on the outcome of the previous decision or chance event.

Question 3

The strategy region graph is a type of sensitivity analysis chart that:

Accepted Answer

The strategy region graph is used to determine the range of input variables where the optimal decision remains the same. It is particularly useful in decision analysis and risk analysis, as it helps in identifying the critical input values and their impact on the decision outcome. The other options are not correct because the EMV sensitivity analysis chart is used to rank the sensitivity of EMV to input variables, and the value of information chart reflects how the value of information changes with probability.

Question 4

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

Accepted Answer

A payoff table is a table that shows the monetary value associated with each possible decision and each possible outcome. Therefore, the statement "For each possible decision and each possible outcome, the payoff table lists the associated monetary value" is true.

Question 5

The risk profile from Precision Tree shows the probability distribution of monetary outcomes in both graphical and tabular form.

Accepted Answer

The statement is correct. The risk profile generated by Precision Tree depicts the possible monetary outcomes in a graphical and tabular way, along with their probability distribution.

Question 6

Expected monetary value (EMV)is:

Accepted Answer

Expected monetary value (EMV) is the weighted average of possible monetary values, weighted by their probabilities. This means that it takes into account not only the value of each possible outcome but also the likelihood of that outcome occurring. Therefore, the best choice would be based on the alternative that has the highest expected monetary value.

Question 7

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

Accepted Answer

Prior probabilities are probabilities assigned before any information is given about the outcome of an uncertainty, while likelihoods are probabilities that are updated based on information about the outcome of an earlier uncertainty.

Question 8

The solution procedure for solving decision trees is called:

Accepted Answer

The solution procedure for solving decision trees is called "folding back," in which we start at the end of the tree and work our way backwards towards the root, calculating the expected value of each node at every stage. Sensitivity analysis, policy iteration, and risk profiling are all related to decision analysis and optimization, but they aren't specific to the solution procedure for decision trees.

Question 9

In general,the expected monetary value (EMV)of a decision will be equal to one of the possible payoffs.

Accepted Answer

The expected monetary value (EMV) is calculated by multiplying the probability of each possible outcome by its monetary value and then adding up all the values. Therefore, the EMV may not necessarily be equal to any one of the possible payoffs.

Question 10

Which of the following statements is true concerning decision tree conventions

Accepted Answer

Decision trees use nodes to represent decision points and branches to represent possible outcomes of decisions. Time does not necessarily have a set direction in a decision tree. The shapes used in a decision tree can vary, but circles are commonly used to represent chance nodes, triangles to represent decision nodes, and ovals to represent end nodes. The probabilities of outcomes are typically displayed on or beneath the end nodes. Therefore, the statement that is true concerning decision tree conventions is that nodes represent points in time (choice C).

Question 11

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

Accepted Answer

This is the correct definition of expected value of information.

Question 12

The denominator of Bayes' rule:

Accepted Answer

The denominator of Bayes' rule decomposes the probability of the new information I into all possibilities, allowing us to adjust our prior probabilities based on the new information. This is essential for Bayesian inference, which updates beliefs based on new evidence.

Question 13

A utility function for risk averse individuals is ____ and/or ____.

Accepted Answer

A risk averse individual prefers less risk and is willing to pay for it. Therefore, their utility function is increasing (more money provides more happiness) and concave (as they gain more money, each additional dollar is worth less to them).

Question 14

The expected monetary value (EMV)criterion represents the long-run average of uncertain outcomes,so it should only be used for recurring decisions.

Accepted Answer

The EMV criterion can be used for both recurring and one-time decisions. It is a useful tool to calculate the potential value of different options based on their probabilities and outcomes.

Question 15

For a risk averse decision maker,the certainty equivalent is less than the expected monetary value (EMV).

Accepted Answer

The certainty equivalent is the guaranteed amount of money that the decision maker is willing to accept instead of taking a risky option with a higher EMV. Since a risk averse decision maker is willing to pay a premium to avoid risk, the certainty equivalent will be less than the EMV.

Question 16

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

Accepted Answer

This definition of certainty equivalent is accurate.

Question 17

The expected value of perfect information (EVPI)is a largely irrelevant concept since perfect information is almost never available at any price.

Accepted Answer

EVPI is a valuable theoretical concept used in decision analysis to measure the maximum amount a decision-maker would be willing to pay for perfect information, helping to understand the value of information and guide investment in information gathering.

Question 18

Bayes' rule is used to:

Accepted Answer

Bayes' rule is a fundamental theorem in probability theory and statistics that allows for the updating of probabilities given new evidence. It is used to update prior probabilities to posterior probabilities after observing new information, effectively "turning around" conditional probabilities to assess the likelihood of various hypotheses given observed evidence. Thus, all the listed options are correct applications of Bayes' rule.

Question 19

All problems related to decision making under uncertainty have three common elements:

Accepted Answer

Decision making under uncertainty involves identifying the available decisions, understanding the possible outcomes of those decisions, and using a value model to predict the results of each decision, thus guiding the decision-making process.

Question 20

Which of the following are probabilities that are conditioned on information that is obtained

Accepted Answer

Posterior probabilities are probabilities that are updated or conditioned on new information or data, making them the best choice for probabilities that are conditioned on information that is obtained. Prior probabilities represent initial beliefs or assumptions about the likelihood of an event, marginal probabilities represent probabilities of an individual event occurring without any additional information, and objective probabilities are based on mathematical principles and not affected by any external factors or information.

Quiz 9: Decision Making Under Uncertainty