2. (40 points) The breakdowns observed in Machine X397 are equally likely to be caused by problems in the motor and the fan. Once the machine has stopped running, there is no way to know what caused the breakdown until a repairman arrives and dismantles the machine. Either one of two repairmen may be called in to fix Machine X397. Of these, Smith charges $300 per repair regardless of the type of the problem. Repairman Jones charges $100 to repair the fan but $400 to repair the motor. Sometimes, Machine X397 makes a noise just prior to breaking down. A motor problem causes a grinding noise 20% of the time, a screeching noise 40% of the time, and no noise 40% of the time. A problem with the fan generates a grinding noise 60% of the time and no noise 40% of the time. All decisions are made by a risk-neutral DM. a. (5 points) Assuming that no one was listening to the machine before it broke down, which repairman should be called in to repair Machine X397? Draw the decision tree. b. (15 points) What is the maximum amount we would consider paying for a round-the-clock recording device that would enable us to monitor the presence and type of noise made by X397? Draw the part of the decision tree where the device is used. C. (10 points) If such a recording device may be bought secondhand for $15, what is our expected cost of maintaining Machine X397? Jones' expected income from repairing Machine X397? Smith's expected income from repairing Machine X397? d. (10 points) Repairman Smith offers to send over his apprentice for $60. The apprentice will dismantle the machine and tell us what he thinks the problem is, after which we may choose to call in either repairman. Should we accept Smith's offer? Draw the part of the decision tree where Smith's apprentice is called. Use the following notation in your answers: A problem with the motor: M A problem with the fan: F Grinding noise: Screeching noise: No noise: G S N 2. (40 points) The breakdowns observed in Machine X397 are equally likely to be caused by problems in the motor and the fan. Once the machine has stopped running, there is no way to know what caused the breakdown until a repairman arrives and dismantles the machine. Either one of two repairmen may be called in to fix Machine X397. Of these, Smith charges $300 per repair regardless of the type of the problem. Repairman Jones charges $100 to repair the fan but $400 to repair the motor. Sometimes, Machine X397 makes a noise just prior to breaking down. A motor problem causes a grinding noise 20% of the time, a screeching noise 40% of the time, and no noise 40% of the time. A problem with the fan generates a grinding noise 60% of the time and no noise 40% of the time. All decisions are made by a risk-neutral DM. a. (5 points) Assuming that no one was listening to the machine before it broke down, which repairman should be called in to repair Machine X397? Draw the decision tree. b. (15 points) What is the maximum amount we would consider paying for a round-the-clock recording device that would enable us to monitor the presence and type of noise made by X397? Draw the part of the decision tree where the device is used. C. (10 points) If such a recording device may be bought secondhand for $15, what is our expected cost of maintaining Machine X397? Jones' expected income from repairing Machine X397? Smith's expected income from repairing Machine X397? d. (10 points) Repairman Smith offers to send over his apprentice for $60. The apprentice will dismantle the machine and tell us what he thinks the problem is, after which we may choose to call in either repairman. Should we accept Smith's offer? Draw the part of the decision tree where Smith's apprentice is called. Use the following notation in your answers: A problem with the motor: M A problem with the fan: F Grinding noise: Screeching noise: No noise: G S N