90-760: Decision & Risk Modeling, AFTERNOON SECTION Midterm, Spring 2016Do not turn the page until you are told to do so. Write your answers below each question.Note how much each problem is worth and budget your time. Total points possible: 110Name: ______________________________Q1: _________ out of 10 possible pointsQ2: _________ out of 15 possible pointsQ3: _________ out of 25 possible pointsQ4: _________ out of 20 possible pointsQ5: _________ out of 30 possible pointsQ6: _________ out of 10 possible pointsTotal Possible Points: 110Question #1: (10 points)Concisely explain the key ideas concerning human judgment & forecasting that are captured by these vignettesdiscussed in the first class. Use neat handwriting. (Verbose or illegible answers will not be graded or will bemarked down sharply.)a) Israeli judges are less likely to grant parole in cases reviewed at the end of the day.b) When guessing the weight of an ox, the average of the guesses of 50 passers-by is often more accuratethan the expert judgment of a butcher. (For non-native English speakers: A butcher is a person whoslaughters animals and sells their meat.)Question #2: (15 points)For the exponential smoothing time-series forecasting method, concisely answer the following in neathandwriting. (Verbose or illegible answers will not be graded or will be marked down sharply.)a) How does one find the parameter ?b) What sort of value for  would you expect if the system generating the time series had been stable for along time?c) What is the relative weight exponential smoothing puts on the 2nd most recent vs. the 4th most recent datapoint? (You must be precise about the algebraic relationships to get credit.) Question #3: (25 points)I ran discriminant analysis with the DA.xla add-in on a data set concerning job applicants and obtained theresults shown below, with some cells deleted.a) Fill in the 8 missing cells in the confusion matrix & also the % correct for the training sample.b) Which group represents the strongest set of candidates?c) Which predictor seems to be the least useful?d) For which classification observations was the group assignment a “close call”?e) How far is Observation #3 in the training sample from the centroid for group #3? Question #4: (20 points)Below is a screen shot of a payoff matrix indicating the cost in dollars for each of 6 alternatives under 4 possiblestates of nature, along with its associated calculations & risk-return frontier plotting standard deviation vs.expected value. a) What number belongs in Cell G4? __________________________________________b) What number belongs in Cell I6? __________________________________________c) Draw a smiley face in the most desirable corner of the risk-return frontier.d) Which option(s) is/are not on this frontier? (Identify them by number.) Question #5: (30 points)A 300-seat theater sells concert tickets three ways: (1) Before the season as part of a season’s ticket package atthe equivalent of $50 per ticket, (2) As individual advance tickets at the “normal” price of $80, and (3) At the“student rush” price ($20) on the day of the show. The season includes six different concerts, each performedjust once, and to keep things simple, suppose there is effectively infinite demand for same-day tickets, so noseat goes empty. The theater needs to decide what is the maximum number of the season’s tickets it should bewilling to sell and, hence, how many seats to hold back so they can be sold as individual tickets or same-daytickets. On the facing page I have pasted the upper left corner of a Monte Carlo simulation to help the theater makeits decision, where demand for individual tickets is modeled as following independent discrete uniform randomvariables between the specified minimum and maximum values (which vary by show). What I have not shownis that the columns extend to the right covering “Sell now” options from 0 up to 210 in steps of 15, and the rowsextend down through row 10,019 to allow for 10,000 simulation trials. a) What problem or kind of problem that we’ve discussed in class does this resemble? b) What is the formula in Cell G1? __________________________________________c) What is the formula in Cell G2? __________________________________________d) What is the formula in Cell G3? __________________________________________e) What is the formula in Cell D9? __________________________________________f) What is the formula in Cell G9? __________________________________________g) What is the formula in Cell G17? __________________________________________h) What is the formula in Cell G19? __________________________________________Question #6: (10 points)Neatly sketch cumulative risk profiles for Option A (Solid line) and Option B (Dashed line) such that: - Option A exhibits 2nd order stochastic dominance over B but not 1st order stochastic dominance. - Option B has a 40% chance of producing negative net revenues.- Neither option has any chance of losing more than $200K or earning more than $500K.- Fully label the axes with both names and numerical values.Also, state the conditions under which the decision maker can safely ignore Option B.