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Statistics
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Write probability statements relating hemline height, stock market prices, and “adventuresomeness” that correspond to the following description of these relationships: Another example is that
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
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
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,
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)
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
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
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
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
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.
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
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
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
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
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
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
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
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.,
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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.
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
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
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