Question 1

__________ is the study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy in the face of uncertainty.
A)Risk analysis
B)Cost analysis
C)Certainty analysis
D)Optimization

Accepted Answer

Risk analysis involves assessing the potential outcomes of a decision in the face of uncertain events or factors. By considering the probability and magnitude of different payoffs, one can make an informed decision that balances risk and reward. Cost analysis, by contrast, is concerned with the financial expenses associated with a decision, while certainty analysis assumes that all factors and outcomes are known with certainty. Optimization involves finding the most efficient or effective solution to a problem, which may or may not take into account risk and uncertainty.

Question 2

Which of the following tools is used to create decision trees in Excel?
A)WhatIf
B)Analytic Solver Platform
C)GoalSeek
D)Data Analysis

Accepted Answer

The Analytic Solver Platform is a comprehensive tool for decision making in Excel, which includes the ability to create decision trees. The other options listed (WhatIf, GoalSeek, Data Analysis) do not have this capability.

Question 3

The parameter R in an exponential utility function represents the
A)decision maker's risk tolerance.
B)utility function's error tolerance.
C)posterior probability.
D)likely profit/loss from the investment.

Accepted Answer

The parameter R in an exponential utility function represents the decision maker's risk tolerance. It reflects the degree to which an individual is willing to take risks in order to achieve higher expected returns. A higher value of R indicates a higher level of risk aversion, while a lower value indicates a greater willingness to take risks.

Question 4

Bayes' theorem
A)can be used only for cases where conditional probabilities are unknown.
B)cannot be used to calculate posterior probabilities.
C)enables the use of sample information to revise prior probabilities.
D)is useful for determining optimal decisions without requiring knowledge of probabilities of the states of nature.

Accepted Answer

Bayes' theorem enables the use of sample information to revise prior probabilities. It allows us to update probabilities based on new information, which can be useful in decision-making and inference. Option A is incorrect because Bayes' theorem can be used when conditional probabilities are known. Option B is incorrect because Bayes' theorem is used to calculate posterior probabilities. Option D is incorrect because Bayes' theorem is not used to determine optimal decisions without knowledge of probabilities of the states of nature.

Question 5

Exponential utility functions assume that the decision maker is
A)a risk monitor.
B)risk averse.
C)risk neutral.
D)a risk taker.

Accepted Answer

Exponential utility functions assume that the decision maker is risk averse, meaning they will always prefer a certain outcome over a risky one with the same expected value. This risk aversion is reflected in the shape of the exponential utility function, which has a concave shape that reflects the diminishing marginal utility of wealth.

Question 6

A __________ is a decision maker who would choose a guaranteed payoff over a lottery with a better expected payoff.
A)risk taker
B)risk-neutral
C)risk avoider
D)risk-creator

Accepted Answer

A risk avoider would choose a guaranteed payoff over a lottery with a better expected payoff because they prefer the safety and certainty of a guaranteed outcome rather than risking the possibility of receiving less or nothing at all.

Question 7

What would be the value added by a market analysis undertaken if the expected value with sample information is $8.56 million and the expected value without sample information is $6.39 million?
A)$8.56 million
B)$6.39 million
C)$2.17 million
D)$14.95 million

Accepted Answer

The value added by a market analysis is the difference between the expected value with sample information and the expected value without sample information, which is $8.56 million - $6.39 million = $2.17 million.

Question 8

New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as
A)joint probability.
B)sample information.
C)conditional probability.
D)expected utility.

Accepted Answer

New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is referred to as sample information. Joint probability refers to the probability of occurrence of two or more events simultaneously. Conditional probability is the probability of an event occurring given that another event has occurred. Expected utility refers to the expected value of the utility function of a particular decision.

Question 9

Using the data below, what would be the joint probabilities, P(U ? S_j)? ? $$\begin{array} { c c c } \begin{array} { c } \text { States of Nature } \ ( s j ) \end{array} & \begin{array} { c } \text { Prior } \ \text { Probabilities } \ P ( s j ) \end{array} & \begin{array} { c } \text { Conditional } \ \text { Probabilities } \ P ( U \mid s j ) \end{array} \ \hline s 1 & 0.65 & 0.75 \ s 2 & 0.20 & 0.35 \ s 3 & 0.15 & 0.20 \ \hline \text { Total } & 1.00 & \ \hline \end{array}$$ A)0.83, 0.12, and 0.05 B)0.49, 0.07, and 0.03 C)0.47, 0.49, and 0.04 D)1.00, 0.59, and 1.00

Accepted Answer

The joint probabilities, P(U and Sj), are calculated by multiplying the prior probabilities of each state, P(Sj), by the conditional probabilities of U given each state, P(U|Sj). For S1, it's 0.65 * 0.75 = 0.4875 (approx. 0.49). For S2, it's 0.20 * 0.35 = 0.07. For S3, it's 0.15 * 0.20 = 0.03.

Question 10

Using the data below, which of the following would be the posterior probabilities, P(S_j| U)? ? ? $$\begin{array} { c c c } \begin{array} { c } \text { States of Nature } \ ( s j ) \end{array} & \begin{array} { c } \text { Prior } \ \text { Probabilities } \ P ( s j ) \end{array} & \begin{array} { c } \text { Conditional } \ \text { Probabilities } \ P ( U \mid s j ) \end{array} \ \hline s 1 & 0.65 & 0.75 \ s 2 & 0.20 & 0.35 \ s 3 & 0.15 & 0.20 \ \hline \text { Total } & 1.00 & \ \hline \end{array}$$ ? A)0.83, 0.12, and 0.05 B)0.49, 0.07, and 0.03 C)0.47, 0.49, and 0.04 D)1.00, 0.59, and 1.00

Accepted Answer

The posterior probabilities, P(Sj|U), can be calculated using Bayes' theorem. For each state of nature Sj, the posterior probability is P(Sj|U) = [P(U|Sj) * P(Sj)] / P(U), where P(U) = Σ[P(U|Si) * P(Si)] for all i. Calculating P(U) = (0.75*0.65) + (0.35*0.20) + (0.20*0.15) = 0.4875 + 0.07 + 0.03 = 0.5875. Then, for each state, P(S1|U) = (0.75*0.65) / 0.5875 = 0.83, P(S2|U) = (0.35*0.20) / 0.5875 = 0.12, and P(S3|U) = (0.20*0.15) / 0.5875 = 0.05.

Question 11

The study of how changes in the probability assessments for the states of nature or changes in the payoffs affect the recommended decision alternative is known as
A)uncertainty analysis.
B)cost analysis.
C)sensitivity analysis.
D)probability analysis.

Accepted Answer

Sensitivity analysis is the study of how changes in the probability assessments or payoffs affect the recommended decision alternative. It helps in identifying which variables have the most impact on the decision and can be used to test the robustness of the recommended decision alternative. Uncertainty analysis and probability analysis are part of sensitivity analysis, but they do not fully encompass the entire concept. Cost analysis is a separate concept that focuses on determining the cost of a particular decision.

Question 12

Which of the following is the value of e, the mathematical constant used in the exponential utility function, U(x) = 1 - e^-^x^/^R? A)3.14159 B)2.71828 C)1 D)The value of e depends on the risk tolerance value.

Accepted Answer

The value of e, the mathematical constant used in the exponential utility function, is known to be approximately equal to 2.71828. Therefore, the correct choice is B.

Question 13

__________ refers to the probability of one event, given the known outcome of a (possibly) related event.
A)Joint probability
B)Priori probability
C)Decisive probability
D)Conditional probability

Accepted Answer

Conditional probability refers to the probability of an event occurring given the occurrence of a related event, whereas joint probability refers to the probability of multiple events occurring simultaneously. Priori probability refers to probability based on prior knowledge or assumptions, and decisive probability is not a common term in probability theory.

Question 14

__________ is a measure of the total worth of a consequence reflecting a decision maker's attitude toward considerations such as profit, loss, and risk.
A)Cost-to-company
B)Utility
C)Decision value
D)Regret

Accepted Answer

Utility is a measure of an individual's satisfaction or happiness with a particular outcome or consequence. It incorporates factors such as profit, loss, and risk, as well as the individual's personal preferences and attitudes. Therefore, it is the most appropriate choice that reflects a decision maker's attitude toward considerations such as profit, loss, and risk.

Question 15

A special case of sample information where the information tells the decision maker exactly which state of nature is going to occur is known as __________ information.
A)perfect
B)mutual
C)conditional
D)prior

Accepted Answer

Perfect information provides complete and accurate knowledge about which state of nature will occur. This allows decision-makers to make optimal decisions since they know exactly what the outcome will be. Mutual information refers to information that is shared between two or more parties, conditional information refers to information that is dependent on some other event or condition, and prior information refers to information that is known before new information is obtained from a sample.

Question 16

The parameter R in the exponential utility function U(x) = 1 - e^-^x^/^R represents the decision maker's risk tolerance. Larger values of R indicate that the decision maker A)is less risk averse (closer to neutral). B)is more risk averse (has less risk tolerance). C)is not concerned with risk. D)will accept the gamble.

Accepted Answer

In the exponential utility function, the parameter R represents the decision maker's risk tolerance. Larger values of R indicate that the decision maker is less risk averse, meaning they are closer to being risk-neutral and more willing to take risks.

Question 17

The weighted average of the payoffs for a chance node is known as the
A)median value.
B)variance of the node.
C)risk measure.
D)expected value.

Accepted Answer

The weighted average of the payoffs for a chance node is known as the expected value. This is a commonly used measure of central tendency in decision tree analysis and is used to calculate the expected outcome of a decision tree pathway.

Question 18

For a particular maximization problem, the payoff for the best decision alternative is $15.7 million while the payoff for one of the other alternatives is $12.9 million. The regret associated with the alternate decision would be
A)$28.6 million.
B)$15.7 million.
C)$0.129 million.
D)$2.8 million.

Accepted Answer

Regret is calculated as the difference between the payoff of the best decision and the payoff of the chosen alternative. Here, it is $15.7 million - $12.9 million = $2.8 million.

Question 19

The utility function for money is a curve that depicts the relationship between
A)decision alternative and utility.
B)branch probabilities and utility.
C)regret and utility.
D)monetary value and utility.

Accepted Answer

The utility function for money depicts the relationship between monetary value and utility. Therefore, the best choice would be based on the option that maximizes monetary value, as this would also maximize utility.

Question 20

__________ refer to the probabilities of the states of nature after revising the prior probabilities based on sample information.
A)Preliminary probabilities
B)Perfect probabilities
C)Joint probabilities
D)Posterior probabilities

Accepted Answer

Posterior probabilities refer to the updated probabilities of the states of nature after taking into consideration the sample information, and are calculated using Bayes' theorem.

Quiz 15: Decision Analysis

__________ is the study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy in the face of uncertainty.

Which of the following tools is used to create decision trees in Excel?

The parameter R in an exponential utility function represents the

Bayes' theorem

Exponential utility functions assume that the decision maker is

A __________ is a decision maker who would choose a guaranteed payoff over a lottery with a better expected payoff.

What would be the value added by a market analysis undertaken if the expected value with sample information is $8.56 million and the expected value without sample information is $6.39 million?

New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as

The study of how changes in the probability assessments for the states of nature or changes in the payoffs affect the recommended decision alternative is known as

Which of the following is the value of e, the mathematical constant used in the exponential utility function, U(x) = 1 - e-x/R?

__________ refers to the probability of one event, given the known outcome of a (possibly) related event.

__________ is a measure of the total worth of a consequence reflecting a decision maker's attitude toward considerations such as profit, loss, and risk.

A special case of sample information where the information tells the decision maker exactly which state of nature is going to occur is known as __________ information.

The parameter R in the exponential utility function U(x) = 1 - e-x/R represents the decision maker's risk tolerance. Larger values of R indicate that the decision maker

The weighted average of the payoffs for a chance node is known as the

For a particular maximization problem, the payoff for the best decision alternative is $15.7 million while the payoff for one of the other alternatives is $12.9 million. The regret associated with the alternate decision would be

The utility function for money is a curve that depicts the relationship between

__________ refer to the probabilities of the states of nature after revising the prior probabilities based on sample information.

Which of the following is the value of e, the mathematical constant used in the exponential utility function, U(x) = 1 - e^-^x^/^R?

The parameter R in the exponential utility function U(x) = 1 - e^-^x^/^R represents the decision maker's risk tolerance. Larger values of R indicate that the decision maker