90-760: Decision & Risk Modeling Midterm Exam, AM Section Spring 2015Do not turn the page until you are told to do so. Note how much each problem is worth and budget your time.Total points possible: 103Name: ______________________________(Write answers in the space provided. If you need more space, you may use additional sheet(s), but be sure toput your name on them and label with the problem number.)Forecasting (21 points)Q1: _________ out of 12 possible pointsQ2: _________ out of 9 possible pointsCategorical Forecasting (25 points)Q3: _________ out of 16 possible pointsQ4: _________ out of 9 possible pointsSimulation (57 points)Q5: _________ out of 12 possible pointsQ6: _________ out of 12 possible pointsQ7: _________ out of 27 possible pointsQ8: _________ out of 6 possible pointsQuestion #1: (12 points)The first two questions pertain to the following spreadsheet for implementing managerial forecasting methodson a stationary time series for weekly sales. (Sales are always integer valued, so the 10 in Week #1 meansexactly 10.0000; it is not a real number that has been rounded off.)Fill in the forecasts the three methods make for Week #15 by placing those values in Cells C22:E22. (Give thenumbers, not the formulas.)Question #2: (9 points)a) Which method gives the best average fit to the historical data?b) Suppose one wished to use Solver to parameterize the 3 Period WMA forecasts. Which cell or cellswould contain the decision variable(s)?c) Which cell or cells would contain the objective function?Question #3: (16 points)I ran discriminant analysis with the DA.xla add-in on a data set (at left below) with 16 past and 5 currentobservations and obtained the results shown (on the right below).a) On the bottom of this page, write out the confusion matrix for this analysis. b) Plot the centroids (as squares) and five classification sample observations (as dots) on the axes providedon the next page. Question #4: (9 points)For the data set graphed below, how would the point at the coordinates (0.18, -0.2) be classified by:a) The k-neighbor rule with k = 1 _________________b) The k-neighbor rule with k = 3 _________________c) The linear discriminant function shown in the graph? _________________Question #5: (12 points)I need to hire a plumber to fix some leaky pipes. The job is big enough that I should get multiple quotes so Ican hire the plumber quoting the lowest price for the job, but it is not clear how many quotes I should obtain.Suppose I believe that the variability from plumber to plumber in prices can be modeled as being normallydistributed with a mean of $500 and a standard deviation of $125 (i.e., 95% of the quotes will be between $250and $750). And suppose that I value the time and hassle of getting a quote and checking out online qualityreviews of the plumber at $20 per quote obtained. Then I can create a Monte Carlo simulation comparing thetotal cost – including both the amount paid to the plumber hired and the monetary value of my time – for thealternative strategies of getting just 1 quote vs. getting 2 quotes, 3 quotes, etc.I created such a simulation. Below is the risk-return frontier obtained for the strategies of getting 1 to 22quotes.a) Augment the frontier with a smiley face indicating the ideal corner.b) If I were risk neutral, which dot on the frontier would I prefer? (Draw an arrow pointing to it)c) If I were risk averse, which dots are not on the efficient frontier because they are dominated by someother strategy? (Circle those dots)d) Indicate on the graph which strategies correspond to which dots. (You don’t need to label all 22. Justlabel enough to make it clear to the graders that you understand which are which.) Question #6: (12 points)I ran a Monte Carlo simulation with 40,000 trials to model the final balance if one invested $100,000 for 10years in a fund whose annual return is normally distributed with a mean of 5% and a standard deviation of 10%.The results are:a) What does the simulation suggest is a 90% confidence interval for the amount of money that will be inthe account after 10 years?b) What does the simulation suggest is a 90% confidence interval for the mean of the distribution? c) What is the probability the fund balance will be $200,000 or greater at the end of the 10 years? Information for Questions #7 and #8Often it is of interest to calculate the distribution of distances between two randomly chosen points. Forexample, consider a rectangular city that is 20 miles east-west and 10-miles north-south. Suppose that at anygiven time the city has one police vehicle that is equally likely to be anywhere in the city and a 911 emergencyoccurs at some other location that is also equally likely to be anywhere in the city. One might be interested inhow far the police must travel to get to the emergency. Here we’ll ask a particular version of this question. How much farther would a police *car* have to travel, ifthe car must move either east-west along streets or north-south on avenues but cannot drive directly toward theemergency by “cutting a diagonal” as opposed to the distance a police helicopter or UAV drone would travel ifit could fly directly to the emergency without having to follow the rectangular street grid? I addressed this by running an MC Simulation with 10,000 trials in the way we’ve been doing in this coursewith a (partial) screen shot as shown below. Question #7: (27 points) What formulas did I use in cells:B8: ________________________________________________________________B9: ________________________________________________________________B12: ________________________________________________________________B14: ________________________________________________________________B16: ________________________________________________________________F2: ________________________________________________________________F3: ________________________________________________________________F6: ________________________________________________________________F19: ________________________________________________________________Question #8: (6 points)The distribution obtained from this simulation is pasted below.a) Would this uncertain quantity be well modeled by a normal random variable?b) Describe in a sentence or two the general shape or meaning of the