Based on minimum expected repair costs, should the new machines be adopted? b. Now you learn that a third plant in a nearby town has been using these machines. They have experienced 6 breakdowns in 3.0 months. Use this information to find the posterior probability that the breakdown rate is 1.5 per month. C. Given your posterior probability, should your company adopt the new machines in order to minimize expected repair costs? d. Consider the information given in part b. If you had read it in the distributor's brochure, what would you think? If you had read it in a trade magazine as the result of an independent test, what would you think? Given your answers, what do you think about using sample information and Bayes' Theorem to find posterior probabilities? Should the source of the information be taken into consideration somehow? Could this be done in some way in the application of Bayes' theorem? Problem 3 - Problem 9.24 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 made the following assessments: There is a 1-in-10 chance that Q will be greater than 0.22, and also a 1-in-10 chance that Q will be less than 0.08. The value for Q is just as likely to be greater than 0.14 as less than 0.14. a. What should your subjective probabilities P10.08 =Q=0.14) and P(0.14 =Q=0.22 be in order to guarantee consistency? b. Use @RISK to find a beta distribution for Q that closely approxi-mates your subjective beliefs. C. The boss tells you that if you expect that the market share will be less than 0.15, the product should not be introduced. Write the boss a memo that gives an expected value and also explains how risky you think it would be to introduce the product. Use your beta approximation. Problem 4 - Problem 9.33 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 asked you how many of these machines you expect to fail while you are out of town, and you have decided to give him your subjective probability distribution. You have made the following assessments: 1. There is a 0.5 chance that none of the machines will fail. e 0.15 chance that tw will fall