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- The project manager of Good Public Relations gatheredthe data shown in Table 7.15 for a new advertisingcampaign.a. How long is the project likely to take? b. What is the probability that the project will take more than38 weeks?c. Consider the path A–E–G–H–J. What is the probability thatthis path will exceed 38 weeks?A construction company needs to move lumber onto the roof of a building. If the lumber falls and hits someone it will cause $1,200,000 in damage. Assume that company must choose between the following levels of precaution: Spend $500 and the probability of an accident is .05 Spend $5,000 and the probability of an accident is .01 Spend $8,000 and the probability of an accident is .008 Spend $10,000 and the probability of an accident is .003 If the construction company is strictly liable for the costs of the accident, how much would they spend on precaution? A. $500 B. $5,000 C. $8,000 D. $10,000An individual has 40,000 in income per year. The person will get sick with probability 0.1. If he does get sick, the medical bills will total 30,000. The following tables shows the utility derived from certain amounts of income: Income Utility40,000 20037,000 19535,000 19030,000 17020,000 14010,000 100Considering the probability of illness, what is the expected utility of income without insurance? Show your work.
- The frequency of breakdown of a machine per month is shown in the table. The cost ofa breakdown is $1,000 and the cost of preventive maintenance is $1,250 per month. Ifpreventive maintenance is performed, the probability of a machine breakdown is negligible. Should the manager use preventive maintenance, or would it be cheaper to repair themachine when it breaks down?Number of breakdowns 0 1 2 3Frequency of occurrence .20 .30 .40 .10Uncertainty The Utility function is U = W1/3Flood occurs with Probabilities=1/25. The Value of a house is $450,000 if no flood. Aftera flood, the value is $50,000. Cost of insurance is 10 cents per dollar.a. Calculate EU b. Calculate EV c. Calculate CE d. Calculate RP e. Calculate the variance and standard deviation f. How much insurance should you buy? Assume your are paying premium in all events.g. What is the expected profit of the insurance company? h. Calculate the coefficient of absolute and relative risk aversion2. Calculate the probabilities that a. the battery life is between 7.5 and 8 hours; and b. the battery life is less than 8 hours. Are these two probabilities different? Explain why or why not. 3. Suppose that you randomly picked 100 iPhones and calculated the average battery life for these phones. Provide your best guess of the value of the average.
- Find the EVPI for the below Payoff table: 162 126 320 194 State of nature 1 2 3 Probabilit y 0.3 0.4 0.3 Acts B 20 0 -20 -50 200 -100 -50 30 400 600 01. A dealer decides to sell a rare book by means of an English auction with a reservation price of 54. There are two bidders. The dealer believes that there are only three possible values, 90, 54, and 45, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue is approximately ______. 2. A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of 5 and the other has a buyer value of 10 and with probability 1/2, one has a buyer value of 8 and the other has a buyer value of 15. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must…Utility Theory You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000. A. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes yourexpected assets after one year.
- example of situations that will you will use empirical, classical, and subjective approach to estimate probabilities.12. Over the last decade, robotic-drone a research and development company has researched in new drone technology for home delivery. Their sales department considers that they could sell as many as $90 million per year with a probability of 20%. With a most likely value of $76 million with a probability of 45% and a lowest value of $50 million. a. Determine the expected value of their sales. b. The sales department estimates that they could maintain this sales rhythm for 4 years with a probability of 67% or that this sales rhythm could be maintained for 8 years. Determine the Expected Value for the PW if the company considers a yearly interest rate of 10%When playing roulette at a casino, a gambler is trying to decide whether to bet $10 on the number 30 or to bet $10 that the outcome is any one of the three possibilities 00, 0, or 1. 3 The gambler knows that the expected value of the $10 bet for a single number is - 53¢. For the $10 bet that the outcome is 00, 0, or 1, there is a probability of 38 of making a net profit of $30 and a probability of losing $10. 35 38 a. Find the expected value for the $10 bet that the outcome is 00, 0, or 1. b. Which bet is better: a $10 bet on the number 30 or a $10 bet that the outcome is any one of the numbers 00, 0, or 1? Why? a. The expected value is $. (Round to the nearest cent as needed.) b. Since the expected value of the bet on the number 30 is C than the expected value for the bet that the outcome is 00, 0, or 1, the bet on is better.