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Making Hard Decisions with decision tools 3rd edition Robert Clemen, Terence Reilly - Solutions

What is the fundamental question that sensitivity analysis answers? Describe the role that sensitivity analysis plays in the development of a requisite decision model?
A friend of yours can invest in a multiyear project. The cost is $14,000.Annual cash flows are estimated to be $5,000 per year for six years but could vary between $2,500 and $7,000. Your friend estimates that the cost of capital (interest rate) is 11%, but it could be as low as 9.5% and as high
Reconsider Hugh Liedtke’s decision as diagrammed in Figure 4.2. Note that three strategies are possible: (1) accept $2 billion, (2) counteroffer$5 billion and then accept $3 billion if Texaco counteroffers, and (3) counteroffer $5 billion and then refuse $3 billion if Texaco counteroffers.
The tax situation for houses with rentals is a bit more complicated than we presented in the chapter. On one hand, Sanjay and Sarah must pay taxes on any rental income, which will increase their expenses. On the other hand, Sanjay and Sarah can depreciate the percentage of the home rented and can
The consequence variable used in the House-Hunting example was Net Annual Cost, but as we mentioned, houses are also purchased as investments, suggesting that it might be useful to include equity and appreciation in the consequence measure.a) In this problem, we will consider the consequence
Some friends of yours have been considering purchasing a new home. They currently live 20 miles from town on a two-acre tract. The family consists of the mother, father, and two small children. The parents also are considering having more children, and they realize that as the children grow, they
Over dinner, your father mentions that he is considering retiring from real-estate sales. He has found a small retail business for sale, which he is considering acquiring and running. There are so many issues to think about, however, that he has a difficult time keeping them all straight. After
When purchasing a home, one occasionally hears about the possibility of “renting with an option to buy. ” This arrangement can take various forms, but a common one is that the renter simply pays rent and may purchase the house at an agreed-upon price. Rental payments typically are not applied
Explain why the lines separating the three regions in Figure 5.11 all intersect at Point D.
Cost-to-loss ratio problem . Consider the decision problem shown in Figure 5.26. This basic decision tree often is called a cost-to-loss ratio problem and is characterized as a decision situation in which the question is whether to take some protective action in the face of possible adverse
The cost-to-loss ratio problem continued . The cost-to-loss ratio problem as shown in Figure 5.26 may be considered a simplified version of the actual situation. The protective action that may be taken may not pro-vide perfect protection. Suppose that, even with protective action, dam-age D will be
An orange grower in Florida faces a dilemma. The weather forecast is for cold weather, and there is a 50% chance that the temperature tonight will be cold enough to freeze and destroy his entire crop, which is worth some $50,000. He can take two possible actions to try to alleviate his loss if the
An important application of sensitivity analysis occurs in problems involving multiple attributes. Many decision makers experience difficulty in assessing trade-off weights. A sensitivity analysis of the trade-off weight, though, can reveal whether a decision maker must make a more precise
Think about organizations in which you have worked, for whom you worked as consultants, or with which you are familiar. What barriers to the implementation of recommendations did you encounter? How would you overcome these barriers? What changes would you make in the decision-making process in
Reconsider the summer-intern decision discussed in Chapter 3. Figure 3.4 shows the fundamental and means objectives. With a group of friends, use these objectives, together with brainstorming, to generate a list of at least 20 things PeachTree can do to help locate and hire a good summer intern.
Describe a situation in which unconscious incubation worked for you. Describe one in which it did not. Can you explain why it worked in the first case but not in the second?
Add ideas of your own to the list in Figure 6.12 concerning methods for reducing risk and adding value.
What are the keys to getting commitment to action from the decision-board participants in the six-step process?
In what quadrant of the grid in Figure 6.2 would you place the following tasks?a. Selecting an investment for the funds in your retirement accountb. Creating an organizational chart for merging two major divisions in an organizationc. Recommending a direction for an organization regarding
Invent another hybrid strategy using the strategy table of Figure 6.9, using what you consider to be the best features of the strategies shown in that figure.Figure 6.9
Choose a decision that you currently face. What are your objectives in this situation? List your means objectives, and for each means objective list at least one alternative that could help achieve that objective.
How would you design an organization so that it could, in Tom Peters’s (1998) words, “thrive on chaos”? What characteristics would such an organization have? What kind of people would you try to hire? How would the role of the managers differ from the traditional view of what a manager does?
The point is often made that formal schooling can actually discourage young children from following their natural curiosity. Curiosity is an important element of creativity, and so it may be the case that schools indirectly and inadvertently cause children to become less creative than they might
Use the means-objectives network in Figure 6.8 to create a list of alternatives for improving automotive safety. Try to create at least one alternative for each objective listed.
Consider the following joint probability distribution for uncertain quantities X and Y:a. Calculate P (Y = 2), P (Y = 2 | X = 2), P (Y = 2 | X = 2), P (Y = 2 | X = 0) b. Calculate P (X = 2), P (X = 2 | Y = 2), P (X = 2 | Y = 0) c. Are X and Y dependent or independent? How would you describe the
Write probability statements relating hemline height, stock market prices, and “adventuresomeness” that correspond to the following description of these relationships: Another example is that high skirt hemlines tend to occur when the stock market is advancing steadily (a bull market), although
Even though we distinguish between continuous and discrete uncertain quantities, in reality everything is discrete if only because of limitations inherent in our measuring devices. For example, we can only measure time or distance to a certain level of precision. Why, then, do we make the
P (A) = 0.68, P (B | A) = 0.30, and P (B | A̅) = 0.02. Find P (A), P (A and B) , and P (A̅ and B). Use these to construct a probability table. Now use the table to find the following:P (B̅| A), P (B̅| A̅), P (B), P (B̅), P (A̅ | B), P (A | B̅), P (A̅ |B̅):
Julie Myers, a graduating senior in accounting, is preparing for an interview with a Big Four accounting firm. Before the interview, she sets her chances of eventually getting an offer at 50%. Then, on thinking about her friends who have interviewed and gotten offers from this firm, she realizes
Find the expected value, variance, and standard deviation of X in the following probability distributions: a. P (X = 1) = 0.05, P (X = 2) = 0.45, P (X = 3) = 0.30, P (X = 4) = 0.20 b. P (X = − 20) = 0.13, P (X = 0) = 0.58, P (X = 100) = 0.29 c. P (X = 0) = 0.368, P (X = 1) = 0.632
If P (X = 1) = p and P (X = 0) = 1 − p, show that E (X) = p and Var (X) = p (1 − p).
If P (A | B) = p, must P (A | B) = 1 − p? Explain.
Suppose that a company produces three different products. The sales for each product are independent of the sales for the others. The information for these products is given in the table that follows:a. What are the expected revenue and variance of the revenue from Product A alone? b. What are the
A company owns two different computers, which are in separate buildings and operated entirely separately. Based on past history, Computer 1is expected to break down 5.0 times a year, with a variance of 6, and costing $200 per breakdown. Computer 2 is expected to break down3.6 times per year, with a
Explain in your own words what an uncertain quantity or random variable is. Why is the idea of an uncertain quantity important in decision analysis?
A firm is negotiating with a local club to supply materials for a party. The firm’s manager expects to sell 100 large bags of pretzels for $3 each or300 for $2 each; these two outcomes are judged to be equally likely. The expected number of bags sold is 200 = (100 + 300) = 2, and expected price
Flip the probability tree shown in Figure 7.22.
Let CP denote carcinogenic potential, TR test results, and FR field results. Suppose that for Figure 7.23 we have the following probabilities:Figure 7.23
The description and statements given in Problem 7.24 often elicit responses that are not consistent with probability requirements. If you are like most people, you ranked statement h (Linda is a bank teller and is active in the feminist movement) as more probable than statement f (Linda is a bank
Suppose you are a contestant on the television game show, Let’s Make a Deal. You must choose one of three closed doors, labeled A, B, and C, and you will receive whatever is behind the chosen door. Behind two of the doors is a goat, and behind the third is a new car. Like most people, you have no
On the fictitious television game show, “Marginal Analysis for Everyone,” the host subjects contestants to unusual tests of mental skill. On one, a contestant may choose one of two identical envelopes labeled A and B, each of which contains an unknown amount of money. The host reveals, though,
Show that if A is independent of B, that is, P (Ai | Bi) = P (Ai) for all possible Outcomes A1, A2,..., An and B1, B 2, ..., B m then B is independent of A, that is, P (Bj | Ai) = P (Bj) for all possible Outcomes A1, A2,..., An and B1 , B2, ..., Bm
Calculate the variance and standard deviation of the payoffs in the final court decision in the Texaco-Pennzoil case as diagrammed in Figure 4.2.
Explain in your own words what an uncertain quantity or random variable is. Why is the idea of an uncertain quantity important in decision analysis?Use the probability table to find the following:
In the oil-wildcatting problem, suppose that the company could collect information from a drilling core sample and analyze it to determine whether a dome structure exists at Site 1. A positive result would indicate the presence of a dome, and a negative result would indicate the absence of a dome.
In Problem 7.30, calculate the probability that the test is positive and a dome structure exists [P (+ and Dome)]. Now calculate the probability of a positive result, a dome structure, and a dry hole [P (+ and Dome and Dry)]. Finally, calculate P (Dome | + and Dry).In problemIn the oil-wildcatting
Referring to the oil-wildcatting decision diagrammed in Figure 7.16, suppose that the decision maker has not yet assessed P(Dome) for Site1. Find the value of P (Dome) for which the two sites have the same EMV. If the decision maker believes that P (Dome) is between 0.55 and0.65, what action should
Again referring to Figure 7.16, suppose the decision maker has not yet assessed P (Dry) for Site 2 or P(Dome) for Site 1. Let P(Dry) = p and P(Dome) = q . Construct a two-way sensitivity analysis graph for this decision problem.Figure 7.16
Refer to Exercises 7.22 and 7.23. Calculate P(FR Positive) and P(FR Positive | TR Positive).Compare P(FR Positive) and P(FR Positive | TR Positive). Would you say that the test results and field results are independent? Why or why not? Discuss the difference between conditional independence and
Use the probability table in Exercise 7.3 to find P(A or B), or the out-come where either A occurs or B occurs (or both).
The Outcome (A or B) sometimes is called the union of A and B. The union event occurs if either Outcome A or Outcome B (or both) occurs. Suppose that both A and B can happen at the same time (i.e., their areas overlap in a Venn diagram). Show that P (A or B) = P (A) + P (B) – P (A and B). Use a
Often it is difficult to distinguish between the probability of anointer section of outcomes (joint probability) and the probability of a conditional outcome (conditional probability). Classify the following as joint probability statements or conditional probability statements. [If in doubt, try to
Calculate the variance and standard deviation of the returns of stocks AB, CD, and EF in the portfolio example of this chapter. See Figure 7.8.Figure 7.8
P (A) = 0.42, P (B | A) = 0.66, and P (B|A¯ ) = 0.25.Find the following:P(A¯ ), P(B¯ | A), P (B¯ |A¯ ), P(B), P(A | B), P (A¯ | B), P (A| B¯ ), P (A¯ | B¯ )
P (A) = 0.10, P (B | A) = 0.39, and P(B | A) = 0.39.Find the following:P(A¯ ), P(B¯ | A), P (B¯ |A¯ ), P (B), P (B¯ ), P (A | B), P (A | B), P (A¯ | B), P (A¯ | B¯ )
Explain in your own words the idea of subjective probability.
It is said that Napoleon assessed probabilities at the Battle of Waterlooin 1815. His hopes for victory depended on keeping the English and Prussian armies separated. Believing that they had not joined forces on the morning of the fateful battle, he indicated his belief that he had a 90% chance of
Should you drop your decision-analysis course? Suppose you faced the following problem: If you drop the course, the anticipated salary in your best job offer will depend on your current GPA: Anticipated Salary | Drop = ($4,000 – Current GPA) + $16,000 If you take the course, the anticipated
Forecasters often provide only point forecasts, which are their best guesses as to an upcoming event. For example, an economic forecaster might predict that U.S. gross national product (GNP) will increase at a3% annual rate over the next three months. Occasionally a forecaster also will provide an
Choose a course that you are currently taking in which the final exam is worth 100 points. Treating your score on the exam as if it were a continuous uncertain quantity, assess the subjective probability distribution for your score. After you have finished, check your assessed distribution for
Compare the discrete-approximation methods by doing the following: a. Use the extended Pearson-Tukey method to create three-point discrete approximations for the continuous distributions assessed in Problem 8.12. Use the approximations to estimate the expected values of the uncertain quantities. b.
Assess the probability that the New York Mets will win the WorldSeries (WS) next year. Call this probability p. Now assess the following probabilities: P(Win WS | Win Pennant) and P(Win Pennant). Use these to calculate q = P(Win WS) = P(Win WS | Win Pennant) P(WinPennant) = P(Win WS and Win
Assess the probability that you will be hospitalized for more than one day during the upcoming year. In assessing this probability, decompose the assessment based on whether or not you are in an auto mobile accident. With this decomposition, you must assess P(Hospitalized | Accident),
Choose a firm in which you are particularly interested, perhaps one where you might like to work. Go to the library and read about this firm, about its industry, and about the relationship of this firm and the industry to the economy as a whole. After your reading, assess a subjective CDF for the
An accounting friend of yours has gone to great lengths to construct a statistical model of bankruptcy. Using the model, the probability that a firm will file for bankruptcy within a year is calculated on the basis of financial ratios. On hearing your explanation of subjective probability, your
Choose a firm in which you are particularly interested, perhaps one where you might like to work. Go to the library and read about this firm, about its industry, and about the relationship of this firm and the industry to the economy as a whole. After your reading, assess a subjective CDF for the
Suppose that you are a solid B student. Your grades in your courses have always been B’s. In your statistics course, you get a D on the midterm. When your parents express concern, what statistical phenomenon might you invoke to persuade them not toworry about the D?
When we assess our subjective probabilities, we are building a model of the uncertainty we face. If we face a range-of-risk problem, and we begin to assess a continuous distribution subjectively, then clearly it is possible to perform many assessments, which would make the sketched CDF smoother and
Most of us have a hard time assessing probabilities with much precision. For instance, in assessing the probability of rain tomorrow, even carefully considering the lotteries and trying to adjust a wheel of for-tune to find the indifference point, many people would eventually say something like
Ellsberg Paradox A barrel contains a mixture of 90 red, blue, and yellow balls. Thirty of the balls are red, and the remaining 60 are a mixture of blue or yellow, but the proportion of blue and yellow is unknown. A sin-gle ball will be taken randomly from the barrel. a. Suppose you are offered the
Explain in your own words the difference between assessing the probability for a discrete event and assessing a probability distribution for a continuous unknown quantity.
Suppose your father asked you to assess the probability that you would pass your decision-analysis course. How might you decompose this probability assessment? Draw an influence diagram to represent the decomposition.
Describe a decomposition strategy that would be useful for assessing the probabilities in Problem 8.7.
In the binomial example with Melissa Bailey, what is the probability that she will be gone six or more weekends?
Typically, the more information we have, the better estimates we can make. However, we mentioned that when using the alternative-parameter method, if we have more assessments than parameters then there may be no single distribution of that type which exactly matches all the assessments. Discuss how
Make the necessary calculations to verify the Empirical Rule for normal distributions, which states that the probability is approximately 0.68 that a normal random variable is within one standard deviation of the mean μ and the probability is approximately 0.95 that the random variable is within
The amount of time that a union stays on strike is judged to follow an exponential distribution with a mean of 10 days.a. Find the probability that a strike lasts less than one day.b. Find the probability that a strike lasts less than six days.c. Find the probability that a strike lasts between six
A photographer works part-time in a shopping center, two hours per day, four days per week. On the average, six customers arrive each hour, and the arrivals appear to occur independently of one another. Twenty minutes after she arrives one day, the photographer wonders what the chances are that
A consumer is contemplating the purchase of a new smart phone. A consumer magazine reports data on the major brands. Brand A has lifetime (TA), which is exponentially distributed with m = 0.2; and Brand B has lifetime (TB), which is exponentially distributed with m = 0.1. (The unit of time is one
On the basis of past data, the owner of an automobile dealership finds that, on average, 8.5 cars are sold per day on Saturdays and Sundays during the months of January and February, with the sales rate relatively stable throughout the day. Moreover, purchases appear to be independent of one
Reconsider your assessed 0.05 and 0.95 fractiles in Problem 8.13.If you are perfectly calibrated when judging these fractiles, then you would expect that in any given situation the actual value has a 0.90 chance of falling between your assessed fractiles (for that variable). a. Assuming you are
In the first eKnow example in which we used binomial probabilities, suppose the results had been that 4 out of the 20 people responded that they would purchase the eKnow. Use Bayes’ theorem to find your posterior probability P (Hit | r = 4; n = 20) for the following pairs of prior
In a city, 60% of the voters are in favor of building a new park. An interviewer intends to conduct a survey. a. If the interviewer selects 20 people randomly, what is the probability that more than 15 of them will favor building the park? b. Instead of choosing 20 people as in part a, suppose that
In bottle production, bubbles that appear in the glass are considered defects. Any bottle that has more than two bubbles is classified as “nonconforming” and is sent to recycling. Suppose that a particular production line produces bottles with bubbles at a rate of 1.1 bubbles per bottle.
Suppose you are interested in an investment with an uncertain return. You think that the return could be modeled as a normal random variable with mean $2,000 and standard deviation $1,500. What is the probability that the investment will end with a loss? What is the probability that the return will
In our discussion of the Poisson distribution, we used this distribution to represent the distribution of positive responses (Definitely Purchase) to the eKnow per hour at the convention booth. Is it reasonable to assume that the Poisson distribution is appropriate for finding the probabilities
You are the mechanical engineer in charge of maintaining the machines in a factory. The plant manager has asked you to evaluate a proposal to replace the current machines with new ones. The old and new machines perform substantially the same jobs, and so the question is whether the new machines are
Sometimes we use probability distributions that are not exact representations of the physical processes that they are meant to represent. (For example, we might use a normal distribution for a distribution of individuals’ weights, even though no one can weigh less than zero pounds.) Why do we do
You are an executive at Procter and Gamble and are about to introduce a new product. Your boss has asked you to predict the market share (Q, a proportion between 0 and 1) that the new product will capture. You are unsure of Q, and you would like to communicate your uncertainty to the boss. You have
Suppose you are considering two investments, and the critical issues are the rates of return (R1 and R2). For Investment 1, the expected rate of return (μ1) is 10%, and the standard deviation (σ1) is 3%. For the second investment, the expected rate of return (μ2) is 20%, and the standard
Your inheritance, which is in a blind trust, is invested entirely in McDonald’s or in U.S. Steel. Because the trustee owns several McDonald’s franchises, you believe the probability that the investment in McDonald’s is 0.8. In any one year, the return from an investment in McDonald’s is
A continuous random variable X has the following density function:a. Draw a graph of this density. Verify that the area under the density function equals 1.b. A density function such as this one is called a uniform density, or sometimes a rectangular density. It is extremely easy to work with
The length of time until a strike is settled is distributed uniformly from0 to 10.5 days.a. Find the probability that a strike lasts less than 1 day.b. Find the probability that a strike lasts less than 6 days.c. Find the probability that a strike lasts between 6 and 7 days.d. Find the conditional
In a survey at a shopping center, the interviewer asks customers how long their shopping trips have lasted so far. The response (T) given by a randomly chosen customer is uniformly distributed from 0 to 1.5 hours. a. Find the probability that a customer has been shopping for 36 minutes or less. b.
If the number of chocolate chips in a chocolate-chip cookie follows a Poisson where the average is 3.6 chocolate chips per cookie, what is the probability of finding no chocolate chips in a given cookie? Fewer than 5 chocolate chips? More than 10 chips?
Phillip Sheridan frequently flies between Washington, D.C. and Raleigh, North Carolina, and as the distance is short, the airline uses turboprop airplanes. He often has a choice between flying on a two-engine or a four-engine airplane. Phillip’s intuition is that the four-engine plane is safer as
To help counselors identify teenagers who may become problem drinkers, a psychologist created a written test and individuals with scores above 75 on this test are flagged as potential problem drinkers. The test was administered to two groups of people: those who have problems with drinking and
A greeting card shop makes cards that are supposed to fit into 6-inch (in.) envelopes. The paper cutter, however, is not perfect. The length of a cut card is normally distributed with mean 5.9 in. and standard deviation 0.0365 in. If a card is longer than 5.975 in., it will not fit into a 6-in.
You are the maintenance engineer for a plant that manufactures consumer electronic goods. You are just about to leave on your vacation for two weeks, and the boss is concerned about certain machines that have been somewhat unreliable, requiring your expertise to keep them running. The boss has
After you have given your boss your information in Problem 9.33, he considers how accurate you have been in the past when you have made such assessments. In fact, he decides you are somewhat optimistic (and he believes in Murphy’s Law), so he assigns a Poisson distribution with m = 1 to the

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