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Q:
Prior probabilities are sometimes called likelihoods, the probabilities that are influenced by information about the outcome of an earlier uncertainty.
Q:
Bayes' rule can be used for updating the probability of an uncertain outcome after observing the results of a test or study.
Q:
The expected value of perfect information (EVPI) is irrelevant concept since perfect information is almost never available at any price.
Q:
The expected value of perfect information (EVPI) is the most the decision maker would be willing to pay for the sample information.
Q:
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.
Q:
The expected value of perfect information (EVPI) is the difference between the EMV with perfect information and the EMV with no additional information.
Q:
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
Q:
The slope of the lines for the input variables on a tornado chart indicates their relative impact on the expected value
Q:
A strategy region chart is useful for seeing whether the decision changes over the range of the input variable.
Q:
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
Q:
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.
Q:
A risk profile lists all possible monetary values and their corresponding probabilities.
Q:
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.
Q:
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.
Q:
If is the monetary value corresponding to outcome i and is its probability, then the expected monetary value is defined as: EMV = .
Q:
In general, the expected monetary values (EMV) represent possible payoffs.
Q:
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.
Q:
In decision trees, a probability node (a circle) is a time when the decision maker makes a decision.
Q:
In decision trees, a decision node (a square) is a time when the result of an uncertain event becomes known.
Q:
Decision trees are composed of nodes (circles, squares, and triangles) and branches (lines).
Q:
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.
Q:
In a single-stage decision problem, a single decision is made first, and then all uncertainty is resolved.
Q:
In making decisions, we choose the decision with the largest expected monetary value.
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
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
Q:
The preferred criterion in decision making is.
a. maximin
b. maximax
c. EMV
d. None of these options
Q:
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
Q:
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
Q:
NARRBEGIN: SA_123_125
Suppose that a decision maker's utility as a function of her wealth, x, is given by U(x) = ln x (the natural logarithm of x).
NARREND
The decision maker now has $15,000 and two possible decisions. For decision 1, she loses $1,000 for certain. For decision 2, she loses $0 with probability 0.9 and loses $4,000 with probability 0.10. Which decision maximizes the expected utility of her net wealth?
Q:
NARRBEGIN: SA_123_125Suppose that a decision maker's utility as a function of her wealth, x, is given by U(x) = ln x (the natural logarithm of x).NARRENDThe 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?
Q:
NARRBEGIN: SA_123_125
Suppose that a decision maker's utility as a function of her wealth, x, is given by U(x) = ln x (the natural logarithm of x).
NARREND
Is this decision maker risk averse? Explain why or why not.
Q:
NARRBEGIN: SA_118_122Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this prospect; the metallurgical properties of the ore and the net price (market price minus mining and transportation costs) of the ore in the future.The metallurgical properties of the ore would be classified as either "high grade" or "low grade". Southport's geologists have estimated that there is a 70% chance that the ore will be "high grade", and otherwise, it will be "low grade". Depending on the net price, both ore classifications could be commercially successful.The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport's economists have simplified the continuous distribution of possible prices into a two-outcome discrete distribution ("high" or "low" net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in millions of dollars), are summarized below.High Grade metallurgy (p=0.7)Low Grade metallurgy (p=0.3)PricesProbabilityOutcomeProbabilityOutcomeHigh0.8$400.6$20Low0.2-$200.4-$40NARRENDShould Southport conduct the imperfect core test if it costs $250,000?
Q:
NARRBEGIN: SA_118_122Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this prospect; the metallurgical properties of the ore and the net price (market price minus mining and transportation costs) of the ore in the future.The metallurgical properties of the ore would be classified as either "high grade" or "low grade". Southport's geologists have estimated that there is a 70% chance that the ore will be "high grade", and otherwise, it will be "low grade". Depending on the net price, both ore classifications could be commercially successful.The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport's economists have simplified the continuous distribution of possible prices into a two-outcome discrete distribution ("high" or "low" net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in millions of dollars), are summarized below.High Grade metallurgy (p=0.7)Low Grade metallurgy (p=0.3)PricesProbabilityOutcomeProbabilityOutcomeHigh0.8$400.6$20Low0.2-$200.4-$40NARRENDSince 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?
Q:
NARRBEGIN: SA_118_122Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this prospect; the metallurgical properties of the ore and the net price (market price minus mining and transportation costs) of the ore in the future.The metallurgical properties of the ore would be classified as either "high grade" or "low grade". Southport's geologists have estimated that there is a 70% chance that the ore will be "high grade", and otherwise, it will be "low grade". Depending on the net price, both ore classifications could be commercially successful.The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport's economists have simplified the continuous distribution of possible prices into a two-outcome discrete distribution ("high" or "low" net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in millions of dollars), are summarized below.High Grade metallurgy (p=0.7)Low Grade metallurgy (p=0.3)PricesProbabilityOutcomeProbabilityOutcomeHigh0.8$400.6$20Low0.2-$200.4-$40NARRENDSuppose that Southport could consider another alternative - postponing the go/no-go decision on the new venture and drilling for a core sample of the ore to determine with complete certainty its metallurgical property. How much should Southport be willing to pay for the core sample?
Q:
NARRBEGIN: SA_118_122Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this prospect; the metallurgical properties of the ore and the net price (market price minus mining and transportation costs) of the ore in the future.The metallurgical properties of the ore would be classified as either "high grade" or "low grade". Southport's geologists have estimated that there is a 70% chance that the ore will be "high grade", and otherwise, it will be "low grade". Depending on the net price, both ore classifications could be commercially successful.The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport's economists have simplified the continuous distribution of possible prices into a two-outcome discrete distribution ("high" or "low" net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in millions of dollars), are summarized below.High Grade metallurgy (p=0.7)Low Grade metallurgy (p=0.3)PricesProbabilityOutcomeProbabilityOutcomeHigh0.8$400.6$20Low0.2-$200.4-$40NARRENDWhat should the Southport do? What is their expected profit?
Q:
NARRBEGIN: SA_118_122Southport Mining Corporation is considering a new mining venture in Indonesia. There are two uncertainties associated with this prospect; the metallurgical properties of the ore and the net price (market price minus mining and transportation costs) of the ore in the future.The metallurgical properties of the ore would be classified as either "high grade" or "low grade". Southport's geologists have estimated that there is a 70% chance that the ore will be "high grade", and otherwise, it will be "low grade". Depending on the net price, both ore classifications could be commercially successful.The anticipated net prices depended on market conditions, and also on the metallurgical properties of the ore. Southport's economists have simplified the continuous distribution of possible prices into a two-outcome discrete distribution ("high" or "low" net price) for the investment analysis. The probabilities of these net prices, and the associated outcomes (in millions of dollars), are summarized below. High Grade metallurgy (p=0.7)Low Grade metallurgy (p=0.3)PricesProbabilityOutcomeProbabilityOutcomeHigh0.8$400.6$20Low0.2-$200.4-$40NARRENDConstruct a decision tree to help Southport identify the strategy that maximizes its expected profit for this investment. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
Q:
NARRBEGIN: SA_113_117
A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each season on a program that turns out to be a flop, and of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops.
NARREND
Should the network purchase the report if it costs $160,000?
Q:
NARRBEGIN: SA_113_117A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each season on a program that turns out to be a flop, and of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops.NARRENDSuppose 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?
Q:
NARRBEGIN: SA_113_117
A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each season on a program that turns out to be a flop, and of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops.
NARREND
The network can conduct market research to determine whether a program will be a hit or a flop. If the market research report is perfectly reliable, what is the most the network should be willing to pay for it?
Q:
NARRBEGIN: SA_113_117
A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each season on a program that turns out to be a flop, and of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops.
NARREND
What should the network do? What is their expected profit?
Q:
NARRBEGIN: SA_113_117A television network earns an average of $1.6 million each season from a hit program and loses an average of $400,000 each season on a program that turns out to be a flop, and of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops.NARRENDConstruct a decision tree to help the television network identify the strategy that maximizes its expected profit in responding to a newly proposed television program. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
Q:
NARRBEGIN: SA_104_112Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Mrs. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.Distribution of Accident Types and Corresponding Damage AmountsType of AccidentConditional ProbabilityDamage to CarMinor0.60$200Moderate0.20$1,000Serious0.10$4,000Catastrophic0.10$30,000NARRENDWhy is there a kink in the line for the "Buy Insurance" line in the above strategy region chart?
Q:
NARRBEGIN: SA_104_112Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Mrs. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.Distribution of Accident Types and Corresponding Damage AmountsType of AccidentConditional ProbabilityDamage to CarMinor0.60$200Moderate0.20$1,000Serious0.10$4,000Catastrophic0.10$30,000NARRENDWhat impact, if any, does the insurance deductible amount have on her decision? Briefly explain your answer
Q:
NARRBEGIN: SA_104_112Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Mrs. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.Distribution of Accident Types and Corresponding Damage AmountsType of AccidentConditional ProbabilityDamage to CarMinor0.60$200Moderate0.20$1,000Serious0.10$4,000Catastrophic0.10$30,000NARRENDWhat impact, if any, does the insurance premium cost have on her decision? Briefly explain your answer
Q:
NARRBEGIN: SA_104_112Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Mrs. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.Distribution of Accident Types and Corresponding Damage AmountsType of AccidentConditional ProbabilityDamage to CarMinor0.60$200Moderate0.20$1,000Serious0.10$4,000Catastrophic0.10$30,000NARRENDWhat impact, if any, does the probability of being in an accident have on her decision? Briefly explain your answer
Q:
NARRBEGIN: SA_104_112Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Mrs. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.Distribution of Accident Types and Corresponding Damage AmountsType of AccidentConditional ProbabilityDamage to CarMinor0.60$200Moderate0.20$1,000Serious0.10$4,000Catastrophic0.10$30,000NARRENDPerform a sensitivity analysis on the optimal decision and summarize your findings. Vary the probability of being in an accident from 0% to 10%, the insurance premium from $50 to $300, and the deductible amount from $0 to $600. In response to which model inputs is the expected total cost value most sensitive?
Q:
NARRBEGIN: SA_104_112Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Mrs. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.Distribution of Accident Types and Corresponding Damage AmountsType of AccidentConditional ProbabilityDamage to CarMinor0.60$200Moderate0.20$1,000Serious0.10$4,000Catastrophic0.10$30,000NARRENDGenerate a statistical summary and risk profile for each of Mrs. Rich's possible decisions. Does this information impact her decision?
Q:
NARRBEGIN: SA_104_112Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Mrs. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.Distribution of Accident Types and Corresponding Damage AmountsType of AccidentConditional ProbabilityDamage to CarMinor0.60$200Moderate0.20$1,000Serious0.10$4,000Catastrophic0.10$30,000NARRENDWhat should Mrs. Rich do? What is her expected cost in that case?
Q:
NARRBEGIN: SA_104_112Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Mrs. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.Distribution of Accident Types and Corresponding Damage AmountsType of AccidentConditional ProbabilityDamage to CarMinor0.60$200Moderate0.20$1,000Serious0.10$4,000Catastrophic0.10$30,000NARRENDConstruct a decision tree to help Mrs. Rich decide whether or not to purchase insurance. Note that the tree should minimize Mrs. Rich's annual expected total cost, including the possible insurance premium, deductible payment, and damage payment. In your tree, make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
Q:
NARRBEGIN: SA_104_112Mrs. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Mrs. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder.Distribution of Accident Types and Corresponding Damage AmountsType of AccidentConditional ProbabilityDamage to CarMinor0.60$200Moderate0.20$1,000Serious0.10$4,000Catastrophic0.10$30,000NARRENDFormulate a payoff table that specifies the cost (in dollars) associated with each possible decision and type of accident.
Q:
NARRBEGIN: SA_102_103
Suppose that a decision maker's risk attitude toward monetary gains or losses x given by the utility function U(x) = NARREND
If there is a 10% chance that one of the decision maker's family heirlooms, valued at $5,000, will be stolen during the next year, what is the most that she would be willing to pay each year for an insurance policy that completely covers the potential loss of her cherished items?
Q:
NARRBEGIN: SA_102_103
Suppose that a decision maker's risk attitude toward monetary gains or losses x given by the utility function U(x) = NARREND Show that this decision maker is indifferent between gaining nothing and entering a risky situation with a gain of $80,000 (probability 1/3) and a loss of $10,000 (probability 2/3).
Q:
NARRBEGIN: SA_97_101
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.
NARRENDShould the credit union purchase the report if it costs $150?
Q:
NARRBEGIN: SA_97_101A 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.NARRENDThe 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?
Q:
NARRBEGIN: SA_97_101A 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.NARRENDWhat should the credit union do? What is their expected profit?
Q:
NARRBEGIN: SA_97_101A 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.NARRENDConstruct 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.
Q:
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.
Q:
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.
Q:
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?