Deck 6: Decision Making Under Uncertainty

Question 1

When the lines for two alternatives cross on a strategy region chart,this shows:

A)A change in which decision alternative is optimal
B)The point at which a decision was made
C)The point where the rate of change in expected value is zero
D)Resolution of the uncertainty about the input variable
E)None of these options

Answer 1

A

Question 2

In decision trees,time:

A)is constant
B)proceeds from bottom to top
C)proceeds from top to bottom
D)proceeds from right to left
E)proceeds from left to right

Answer 2

E

Question 3

The solution procedure that was introduced in the book for decision trees is called the:

A)folding diagram
B)single-stage method
C)risk profile method
D)precision tree method
E)folding back on the tree

Answer 3

E

Question 4

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

A)The height of the line above the horizontal axis for each variable
B)The length of the line for each variable
C)The slope of the line for each variable
D)The color of the line for each variable
E)None of these options

Question 5

A payoff table lists the monetary values (profit or loss)for each possible _____and each possible _____.

A)mean and standard deviation
B)decision and utility
C)decision and outcome
D)risk profile and outcome
E)None of these options

Question 6

In decision trees,probabilities are listed on probability branches.These probabilities may be _____ events that have already been observed.

A)marginal due to
B)conditional on
C)averaged with
D)increased by
E)the same as

Question 7

If all monetary values in a decision problem are costs,then it is customary to list them as __________ values in a cost table.

A)positive
B)negative
C)either positive or negative
D)All of these options

Question 8

Bayes' Rule is useful for?

A)Value of Sample Information
B)Value of Perfect Information
C)Sensitivity Analysis
D)All of these options
E)None of these options

Question 9

There are three types of nodes that are used with the decision trees.They are the:

A)mean nodes,variance nodes,and the standard deviation nodes
B)probability nodes,risk nodes,and the expected value nodes
C)supply nodes,demand nodes,and the expected value nodes
D)decision nodes,probability nodes,and end nodes.
E)horizontal nodes,vertical nodes,and the diagonal nodes

Question 10

Which of the following can be obtained with a tornado chart?

A)The absolute change in expected value resulting from the change in each input variable
B)The percent change in expected value resulting from the change in each input variable
C)A ranking of the relative sensitivity of expected value to each input variable
D)None of these options
E)All of these options

Question 11

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

A)the mean,median,and mode
B)the set of decisions,the cost of each decision and the profit that can be made from each decision
C)the set of possible outcomes,the set of decision variables and the constraints
D)the set of decisions,the set of possible outcomes,and a value model that prescribes results
E)None of these options

Question 12

Which of these sensitivity analysis charts is most useful in determining whether the optimal decision changes over the range of the input variable?

A)Strategy region chart
B)Tornado chart
C)Spider chart
D)All of these options
E)None of these options

Question 13

In a single-stage decision tree problem,all ___________ are made first and then all ___________ is (are)resolved.

A)decisions; uncertainty
B)calculations; probabilities
C)EMV calculations; posterior probabilities
D)likelihoods; posterior probabilities
E)prior probabilities; joint probabilities

Question 14

Which of the following is true with regard to a good decision?

A)It ensures that good outcomes will be obtained
B)It accounts for unlucky outcomes
C)It should be independent of the sequencing of uncertainties and decisions
D)It should incorporate all information about uncertainties and alternatives
E)All of these options

Question 15

The preferred criterion in decision making is.

A)maximin
B)maximax
C)EMV
D)None of these options

Question 16

Which of the following statements are true?

A)Sensitivity analysis is a process of seeing how optimal decision and EMV vary when one or more inputs vary.
B)Multistage decision problem is one where decisions and observations of uncertain outcomes alternate.
C)Contingency plan is a strategy in a multistage decision problem that specifies which decision to make for each possible outcome.
D)All of the above
E)None of the above

Question 17

The expected value of sample information (EVSI)is equal to:

A)EMV with posterior information - EMV with prior information
B)EMV with free perfect information - EMV free information
C)EMV with perfect information - EMV without information
D)EMV with free information - EMV without information
E)None of these options

Question 18

Expected monetary value (EMV)is:

A)the average or expected value of the decision if you knew what would happen ahead of time
B)the weighted average of possible monetary values,weighted by their probabilities
C)the average or expected value of the information if it was completely accurate
D)the amount that you would lose by not picking the best alternative
E)a decision criterion that places an equal amount on all states of nature

Question 19

A risk profile lists:

A)all possible monetary values and their corresponding probabilities
B)all possible outcomes and their corresponding utility
C)all options and their possible outcomes
D)the nodes and branches for each possible outcome
E)None of these options

Question 20

In the nomenclature of Bayes' Rule,which of the following are probabilities that are conditioned on information that is obtained?

A)Prior probabilities
B)Posterior probabilities
C)Marginal probabilities
D)Objective probabilities
E)Subjective probabilities

Question 21

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

Question 22

One class of "ready-made" utility functions is called exponential utility.Exponential utility has an adjustable parameter called risk tolerance.The risk tolerance parameter measures:

A)how much money the decision maker has to spend
B)the decision maker's attitude toward risk
C)how much risk there is in a given decision
D)the probability of an unfavorable outcome
E)None of these options

Question 23

With regard to decision making,most individuals are __________________.

A)risk averse
B)risk seekers
C)risk maximizers
D)EMV maximizers
E)None of these options

Question 24

The expected value of perfect information (EVPI)is equal to:

A)EMV with posterior information - EMV with prior information
B)EMV with free perfect information - EMV with information
C)EMV with free perfect information - EMV with no information
D)EMV with perfect information - EMV with less than perfect information

Question 25

Utility functions are mathematical functions that transform monetary values - payoffs and costs - into ________________.

A)expected values
B)utility values
C)EMV values
D)anchor values
E)None of the above

Question 26

In a single-stage decision problem,a single decision is made first,and then all uncertainty is resolved.

Question 27

In making decisions,we choose the decision with the largest expected monetary value.

Question 28

In decision trees,a decision node (a square)is a time when the result of an uncertain event becomes known.

Question 29

Mathematically,the utility function for risk adverse individuals is said to be _____________ and/or _______________.

A)decreasing ,linear
B)decreasing ,convex
C)increasing ,linear
D)increasing ,concave
E)increasing ,decreasing

Question 30

A risk profile lists all possible monetary values and their corresponding probabilities.

Question 31

When you use the expected monetary value (EMV)criterion,you are not using all of the information that is shown in the risk profiles of alternatives,since you are only comparing the means.

Question 32

For each possible decision and each possible outcome,the payoff table lists the monetary value earned by an organization,where a positive value represents a profit and a negative value represents a loss.

Question 33

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

Question 34

In decision trees,an end node (a triangle)indicates that the problem is completed; that is,all decisions have been made,all uncertainty has been resolved,and all payoffs/costs have been incurred.

Question 35

Tornado charts and spider charts can be used to determine which input variables have the most impact on the expected value in a decision problem

Question 36

If is the monetary value corresponding to outcome i and is its probability,then the expected monetary value is defined as: EMV = .

Question 37

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

Question 38

The expected monetary value (EMV)criterion is sometimes referred to as "playing the averages" and for that reason should only be used for recurring decisions.

Question 39

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.

Question 40

If x is a monetary value (a payoff if positive,a cost if negative),U(x)the utility of this value,and R > 0 is an adjustable parameter called the risk tolerance,then the function U(x)= 1 - is called

A)Poisson utility
B)exponential utility
C)binomial utility
D)normal utility

Question 41

(A)Construct a decision tree to help the landowner make her decision.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.
(B)What should the landowner do? Why?
(C)Suppose the landowner is uncertain about the reliability of her geologist friend's estimate of the probability that oil will be found on her land.If she thinks the probability could be anywhere between 40% and 80%,would that change her decision?
(D)Suppose that,in addition to the uncertainty about the probability of finding oil,the landowner is also uncertain about the cost of the exploratory well (could vary +/- 25%)and the future profits (could vary +/- 50%).To which of these variables is the expected value most sensitive?
(E)What does the risk profile show about the relative risk levels for the landowner's two options?
(F)Suppose the landowner suspects that she may be a somewhat risk-averse decision maker,because the she doesn't feel there is as much of a difference between the two options as their expected values would indicate.She consults with a decision analysis expert who asks her to decide between two hypothetical alternatives: 1)a gamble with equal probabilities of winning an amount $X and losing an amount -$X/2,and 2)doing nothing,with a payoff of $0.The point at which she cannot decide between 1)and 2)is when X=$1,500,000.What is her risk tolerance if she uses an exponential utility function to model her preferences?
(G)Apply the risk tolerance given in your answer to the previous question to the landowner's decision tree in (A).What is the optimal decision in this case? What is the resulting certainty equivalent?
(H)If the landowner could hire an expert geologist prepare a report to help her make her decision,what is the most that information could be worth? Assume the geologist's information is perfectly reliable.

Question 42

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

Question 43

Utility function is a function that encodes a person's or company's feelings toward risk.

Question 44

The slope of the lines for the input variables on a tornado chart indicates their relative impact on the expected value

Question 45

(A)Construct a decision tree to help the power company decide what to do.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.
(B)Where should the power company build the plant? What is the expected cost?
(C)Suppose that a geologist (and his team)can be hired to analyze the fault structure at Chico Canyon.He will either predict whether an earthquake will occur or not.If the geologist is perfectly reliable,what is the most the company should be willing to pay for his services?
(D)Suppose that an actual (not perfectly reliable)geologist can be hired to analyze the earthquake risk.The geologist's past record indicates that he will predict an earthquake on 90% of the occasions for which an earthquake will occur and no earthquake on 85% of the occasions for which an earthquake will not occur.Given this information,what are the posterior probabilities that an earthquake will and will not occur,given the geologists predictions?
(E)Should the company hire the geologist if his fee is $1.5M?

Question 46

The expected value of perfect information (EVPI)is the most the decision maker would be willing to pay for the sample information.

Question 47

Tyson Manufacturing (a maker of industrial products)is interested in marketing a new product.The company must decide whether to manufacture this product essentially on its own or employ a subcontractor to manufacture it.Below are two tables that represent the information related to the estimated probability distribution of the cost of one unit of this product under each alternative.
Assuming that Tyson seeks to minimize the expected unit cost of manufacturing of buying the new product,should the company make the new product or buy it from a subcontractor? Show your work.

Question 48

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

Question 49

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

Question 50

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

Question 51

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

Question 52

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.

Question 53

(A)Construct a decision tree to help her model her option decision making.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.
(B)What is the optimal decision making policy regarding the options in all possible scenarios over the next two years?
(C)What is the expected value of the stock options? Ignore the time value of money (assume no discounting of future payoffs)
(D)If her estimates of the increases/decreases or probabilities are inaccurate,could the options have a negative EMV?

Question 54

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

Question 55

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

Question 56

Rational decision makers are never willing to violate the expected monetary value (EMV)maximization criterion when large amounts of money are at stake.

Question 57

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

Question 58

(A)Construct a decision tree to help the company make its decision.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.
(B)What is the best lease option? Why?
(C)Suppose the company could hire an experienced mechanic to inspect the old grader to determine the repair cost before the company makes its final decision.If the mechanic is always correct in his assessments,what is the most the company would pay for the inspection?

Question 59

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

Question 60

(A)Construct a decision tree to help the investor make his decision.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.
(B)What is the best choice for the investor? Why?
(C)Suppose that investor has an exponential utility function for final assets with a risk tolerance parameter equal to $60,000.Which investment opportunity will he prefer in this case? What is his certainty equivalent?

Question 61

What should the credit union do? What is their expected profit?

Question 62

The station is most uncertain about the average monthly revenue associated with the rock format and an A1 audience.Construct a strategy region chart for this input variable with a possible range from $85,000 to $200,000.Does the optimal decision to select the country format change at any point in this range?

Question 63

Formulate a payoff table that specifies WTC's payoff (in dollars)associated with each possible decision and each market condition in the future.

Question 64

Construct a decision tree to identify the buyer's course of action that maximizes the expected profit earned by the chain from the purchase and subsequent sale of footballs in the coming year.

Question 65

What are the expected payoffs for the three alternatives?

Question 66

As the average monthly revenue associated with the rock format and an A1 audience varies between $85,000 to about $140,000,what happens to the maximum expected revenue? Briefly explain why.

Question 67

What is the probability that a randomly selected individual from this population earns less than $50,000 per year?

Question 68

What course of action is optimal for WTC? What is the expected profit in that case?

Question 69

What format is optimal? What is the expected profit in that case?

Question 70

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.

Question 71

Formulate a payoff table that specifies the contribution to profit (in dollars)from the sales of footballs by this chain for each possible purchase decision (in hundreds of pairs)and each outcome with respect to consumer demand.

Question 72

What else might one consider in choosing from among these alternatives?

Question 73

Generate a risk profile for each possible decision in this problem.Would this have any impact on your decision?

Question 74

Construct a decision tree to help the credit union decide whether or not to make the loan.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.

Question 75

Construct a decision tree to identify the course of action that maximizes WTC's expected profit.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.

Question 76

What is the optimal strategy for order quantity,and what is the expected profit in that case?

Question 77

If a randomly selected individual is observed to earn at least $50,000 per year,what is the probability that this person is a man?

Question 78

As the average monthly revenue associated with the rock format and an A1 audience varies between about $142,500 and $200,000,what happens to the maximum expected revenue? Briefly explain why.

Question 79

If a randomly selected individual is observed to earn less than $50,000 per year,what is the probability that this person is a woman?

Question 80

Generate a risk profile for each of WTC's possible decisions in this problem.Characterize the differences in risk for the different options.