6. (15) A individual, with a utility function InW and an initial wealth level Wo, is faced with afair gamble of winning or losing Sh (where Wo > h> 0) with 50-50 chance.(a) Is this individual risk averse? Explain.(b) Suppose that the individual is willing to pay up to an amount of f in order to avoid such agamble. Give the equation that determines f, and solve the equation for f (i.e., express fin termsof Wo and h).(c) Show that fincreases as h increases.

a) An individual who always refuses fair bets is said to be risk averse. If individualsexhibit a…

Answered: 6. (15) A individual, with a utility…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2. A leading researcher in the study of interstate highway accidents proposes that a major cause of many collisions on the interstates is not the speed of the vehicles but rather the difference in speeds of the vehicles. When some vehicles are traveling slowly while other vehicles are traveling at speeds greatly in excess of the speed limit, the faster-moving vehicles may have to change lanes quickly, which can increase the chance of an accident. Thus, when there is a large variation in the speeds of the vehicles in a given location on the interstate, there may be a larger number of accidents than when the traffic is moving at a more uniform speed. The researcher believes that when the standard deviation in speed of vehicles exceeds 10 mph, the rate of accidents is greatly increased. During a 1-hour period of time, a random sample of 50 vehicles is selected from a section of an interstate known to have a high rate of accidents, and their speeds are recorded using a radar gun. The data…
Hemmingway, Inc., is considering a $5 million research and development (R&D) project. Profit projections appear promising, but Hemmingway's president is concerned because the probability that the R&D project will be successful is only 0.50. Furthermore, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $20 million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized. Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated $25 million. Under this option, the company would not build the $20 million production facility. The decision tree is shown in Figure 4.16. The profit projection for each outcome is shown at the end of the branches. For example, the revenue projection for the high demand outcome is $59 million.…
32. A hardware company sells a lot of low-cost, highvolume products. For one such product, it is equallylikely that annual unit sales will be low or high. Ifsales are low (30,000), the company can sell theproduct for $20 per unit. If sales are high (70,000),a competitor will enter and the company will be ableto sell the product for only $15 per unit. The variablecost per unit has a 20% chance of being $10, a 60%chance of being $11, and a 20% chance of being $12.Annual fixed costs are $20,000.a. Use simulation to estimate the company’s expectedannual profit.b. Find a 95% interval for the company’s annualprofit, that is, an interval such that about 95% ofthe actual profits are inside it.c. Now suppose that annual unit sales, variable cost,and unit price are equal to their respective expectedvalues—that is, there is no uncertainty. Determinethe company’s annual profit for this scenario.d. Can you conclude from the results in parts a and cthat the expected profit from a simulation is…
You are considering purchasing stand-alone shares in two companies: Company A and Company B. While both companies expect a rate of return of 15% under normal market conditions, the possible returns under strong and weak economies differ. There is a 30% chance of a weak economy outcome, a 30% chance of a strong economy outcome, and a 40% chance of a normal outcome. For Company A, under a strong economy, they expect a return of 75%. Under a weak economy, they expect a return of -45%. For Company B, under a strong economy, they expect a return of 23%. Under a weak economy, they expect a return of 7.5%. 1. Create a probability distribution table for both companies. 2. Calculate the standard deviation for both companies. 3. With the distribution, create either a bar graph or a bell curve to graph the two companies. 4. From your calculations, describe which company you would consider investing in, if you were risk averse.
In general, ___________% of the values in a data set lie at or below the 28 th percentile. _______________ % of the values in a data set lie at or above the 90 th percentile.. If a sample consists of 700 test scores, _________of them would be at or below the 52 th percentile. If a sample consists of 700 test scores, ________ of them would be at or above the 64 th percentile.
Mike, a lumber wholesaler, is considering the purchase of a (railroad) car- load of varied dimensional lumber. He calculates that the probabilities of reselling the load for $10,000, $9000, and for $8000 are 0.22, 0.33, and 0.45 respectively. In order to ensure an expected profit of $3000, how much can Mike pay for the load
An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns. What are the (x,y) values? What is the optimal profit?
An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns.(x, y)= What is the optimal profit?$
I have two questions. 1) Will improving customer service result in higher stock prices for the companies providing the better service? "When a company's satisfaction score has improved over the prior year's results and is above the national average (75.6), studies show its shares have a good chance of outperforming the broad stock market in the long run." The following satisfaction scores of three companies for the 4th quarters of two previous years were obtained from an economic indicator. Assume that the scores are based on a poll of 50 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 6 points in each case. Company Year 1 Year 2 Company A 73 76 Company B 75 77 Company C 77 78 (a) For Company A, is the increase in the satisfaction score from year 1 to year 2 statistically significant? Use ? = 0.05. (Let ?1 = the satisfaction score for year 2 and ?2 = the satisfaction score for year 1.)…
2–42. Credit derivatives are a new kind of investment instrument: they protectinvestors from risk.9 If such an investment offered by ABN Amro has a 90% chanceof making money, another by AXA has a 75% chance of success, and one by the INGGroup has a 60% chance of being profitable, and the three are independent of eachother, what is the chance that at least one investment will make money?
A citrus grower anticipates a profit of $100,000 this year if the nightly temperatures remain mild. Unfortunately, the weather forecast indicates a 25% chance that the temperatures will drop below freezing during the next week. Such freezing weather will destroy 40% of the crop and reduce the profit to $60,000. However, the grower can protect the citrus fruit against the possible freezing (using smudge pots, electric fans, and so on) at a cost of $5000. Should the grower spend the $5000 and thereby reducethe profit to $95,000? [Hint: Compute E(X ), where X is theprofit the grower will get if he does nothing to protect the fruit.]
Suppose that speeding imposes externalities on other people resulting in a social cost of $50. A town is considering hiring an extra police officer to give out speeding tickets. If we want to maximize social welfare (absent enforcement costs), which of the following statements are true? (Assume risk neutral drivers.) a) If the probability of detection with the extra police officer is 10%, then a speeding ticket should cost $55. b) If the probability of detection with the extra police officer is 10%, then a speeding ticket should cost $500. c) If the probability of detection with the extra police officer is 100%, then no one will speed. d) If the probability of detection with the extra police officer is 90%, then a speeding ticket should cost $59 e) None of the above

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