Bayes rule and tree pruning.docx

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ignore ( 1.A consumer electronics company is considering marketing a new model of TV screen. In the past 40% of the TV screens marketed by the company have been successful. Before marketing the latest screen, the marketing research department conducts an extensive study. The report will be either favorable or unfavorable to the introduction. In the past, 80% of the successful TV screens had gotten a favorable report, and 30% of the unsuccessful screens had gotten a favorable report. )

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BUS 190 Homework 11 - Decision Theory Bayes’ Rule problems 1. A consumer electronics company is considering marketing a new model of TV screen. In the past 40% of the TV screens marketed by the company have been successful. Before marketing the latest screen, the marketing research department conducts an extensive study. The report will be either favorable or unfavorable to the introduction. In the past, 80% of the successful TV screens had gotten a favorable report, and 30% of the unsuccessful screens had gotten a favorable report. a. What are the prior probabilities (use notation as in class)? b. What are the given conditional probabilities (use notation as in class)? c. What is the resulting probability tree? d. Use the tree above to find the probability that the new screen will be successful if the marketing research issues a favorable report. (hint: put all the English wording into notation. They will involve conditional probabilities. Use the definition of conditional probability and the tree to find the necessary conditional probabilities. ) e. Use the tree above to find the probability that the new screen will be successful if the marketing research issues an unfavorable report? Use the probability tree above to work out your answer. 2. Olive Construction Company is determining whether it should submit a bid for a new shopping center. In the past, Olive’s main competitor, Base Construction Company, has submitted bids 70% of the time. If Base company does not bid on a job, the probability that Olive Construction Company will get the job is 50%. If Base Construction bids on the job, the probability that Olive will get the job is 25%. a. What are the prior probabilities (use notation as in class)? b. What are the given conditional probabilities (use notation as in class)? c. What is the resulting probability tree? d. Use your tree to calculate the following: If Olive gets the job, what is the probability that Base Construction did not bid? e. What is the probability that if Olive gets the job, Base Construction did bid? f. What is the probability that Olive gets the job? 3. (Decision theory redux – the whole thing put together, including Bayes) A machine shop owner is attempting to decide whether ot purchase a new drill press, a lathe, or a grinder. The return from each will bet determined by whether the company succeeds in getting a government military contract. The profit or loss from each purchase and probabilities associated with each contract outcome are shown in the following payoff table. Note: Probability or getting a contract is 0.40 Purchase Drill press Lathe Grinder a. Contract No Contract $40,000 ($8,000) $20,000 $4,000 $12,000 $10,000 Which are the decisions? b. Which are the states of nature? c. On a separate sheet of paper, draw the decision tree for this problem, paying attention to the proper nodes. You will be drawing an augmented tree later, so this tree should take up 1/3 the page or less. d. Calculate the EV for each decision on the right hand side of the tree. e. What is your best decision? f. Calculate the EV OF PI. (this means you have to also calculate EV with PI and EV without PI) The machine shop owner is considering hiring a consultant with ties to the military to ascertain whether or not the shop will get the contract. The consultant is a former military officer who uses personal contacts in the military to find out such information. After talking to other shop owners who have hired this consultant, the owner has found he has a probability of .7 of getting a favorable report from the consultant, given that the contract is awarded to the shop, and a probability of .8 of getting an unfavorable report, given that the contract is not awarded. . g. There are conditional probabilities given in the above description. If we denote favorable by F and unfavorable by U, and A for contracted awarded and N for contract not awarded, which of the following gives the proper notation? P(A|F) or P(F|A)? P(N|U) or P(U|N)? What are the values for the conditional probabilities you were given ?(give that with P(X|Y) = n, not just the number n) h. Use Bayes Rule to calculate P(F), P(U), P(A|F), P(A|U), P(N|F) and P(N|U).Use a probability tree for your work. Show ALL your work below. i. Use your probabilities from g to draw an augmented tree. The shop owner has to decide whether to hire the consultant or not. The original tree was without a consultant. The new part of the tree will reflect the decisions he has to make WITH a consultant. This should parallel the trees we have done in class. Draw this on the same sheet of paper as the original tree for this problem. j. “Prune” the tree by calculating the relevant EVs and making the relevant decisions. Show these on your tree. If you need extra space for work, show it below, but label which node you are working on. k. Determine the optimal decision strategy. l. What is the EV OF SI for this problem? (note: you have to calculate EV with SI and EV wo SI) m. What is the efficiency of sample information for this problem?
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