stb answer all correctly123

22. QUESTION: Three prisoners, A, B, and C, are held in separate cells. Two are to be executed. The warder knows specifically who is to be executed, and who is to be freed, whereas the prisoners know only that two are to be executed. Prisoner A reasons as follows: my probability of being freed is clearly 1 3 until I receive further information. However, it is clear that at least one of B and C will be executed, so I will ask the warder to name one prisoner other than myself who is to be executed. Once I know which of B and C is to be executed, either I will go free or the other, unnamed, prisoner will go free, with equal probability. Hence, by asking the name of another prisoner to be executed, I raise my chances of survival from 1 3 to 1 2 . Investigate A's reasoning.

The question is well.

18. QUESTION: Two events A and B are such that P(A) = 0.5, P(B) = 0.3 and P(A B) = 0.1. Calculate (a) P(A|B); (b) P(B|A); (c) P(A|A B); (d) P(A|A B); (e) P(A B|A B).

15I have in my pocket ten coins. Nine of them are ordinary coins with equal chances of coming up head and tail when tossed and the tenth has two heads. (a) If I take one of the coins at random from my pocket, what is the probability that it is the coin with two heads ? (b) If I toss the coin and it comes up heads, what is the probability that it is the coin with two heads ? (c) If I toss the coin one further time and it comes up tails, what is the probability that it is one of the nine ordinary coins ?

16. QUESTION: Let A, B and C be any three events. Draw Venn diagrams to deduce that (a) A (B C) = (A B) (A C); (b) (A B) = A B ; (c) (A B) = A B

17. QUESTION: A certain person considers that he can drink and drive: usually he believes he has a negligible chance of being involved in an accident, whereas he believes that if he drinks two pints of beer, his chance of being involved in an accident on the way home is only one in five hundred. Assuming that he drives home from the same pub every night, having drunk two pints of beer, what is the chance that he is involved in at least one accident in one year? Are there any assumptions that you make in answering the question?

21. QUESTION: In a certain town, 30% of the people are Conservatives; 50% Socialists; and 20% Liberals. In this town at the last election, 65% of Conservatives voted, as did 82% of the Socialists and 50% of the Liberals. A person from the town is selected at random, and states that she voted at the last election. What is the probability that she is a Socialist?

23. QUESTION: You're playing duplicate bridge. Your partner has bid two spades, and you have to decide whether to pass or to bid game in spades, namely to bid four spades. You reckon that there is a good chance, 40%, that four spades will make. Otherwise, you think three spades will make about 40% of time, and two spades the rest of the time. Suppose there are no doubles (by the opposition, for penalties). The gains and losses depend on whether you are vulnerable or not. The possible outcomes and scores are as follows: Not vulnerable Vulnerable Score if you make Score if you make You bid 2 spades 3 spades 4 spades 2 spades 3 spades 4 spades 2 spades 110 140 170 110 140 170 3 spades -50 140 170 -100 140 170 4 spades -100 -50 420 -200 -100 620 What should you bid when not vulnerable? What should you bid when vulnerable? Calculate the variation in score for one of the bids.

24. QUESTION: Tay-Sachs disease is a rare fatal genetic disease occurring chiefly in children, especially of Jewish or Slavic extraction. Suppose that we limit ourselves to families which have (a) exactly three children, and (b) which have both parents carrying the Tay-Sachs disease. For such parents, each child has independent probability 1 4 of getting the disease. Write X to be the random variable representing the number of children that will have the disease. (a) Show (without using any knowledge you might have about the binomial distribution!) that the probability distribution for X is as follows: 9

. QUESTION: A six-sided die has four green and two red faces and is balanced so that each face is equally likely to come up. The die will be rolled several times. Suppose that we score 4 if the die is rolled and comes up green, and 1 if it comes up red. Define the random variable X to be this score. Write down the distribution of probability for X and calculate the expectation and variance for X.

27. QUESTION: X takes values 1, 2, 3, 4 each with probability 1/4 and Y takes values 1, 2, 4, 8 with probabilities 1/2, 1/4, 1/8 and 1/8 respectively. Write out a table of probabilities for the 16 paired outcomes which is consistent with the distributions of X and Y . From this find the possible values and matching probabilities for the total X + Y and confirm that E(X + Y ) = E(X) + E(Y ).

A wholesaler supplies products to 10 retail stores, each of which will independently make an order on a given day with chance 0.35. What is the probability of getting exactly 2 orders? Find the most probable number of orders per day and the probability of this number of orders. Find the expected number of orders per day.

Due to his long hours as a junior broker with Stampson, Clarke & Weinstein, a prestigious blue-chip brokerage firm on Wall Street, Mike Keaggy was put on some substantive accounts that pertained to the firm's top corporate clients. Just several weeks ago, Mike's boss, Harry Stampson, a named partner, approached Mike about taking on the Pfeifer account. The Pfeifer Corporation, a closely-held corporation of several brothers and sisters of a wealthy California family, had generated approximately $1.7 million in annual fees over the past ten years, and was an account that was assigned to promising your workers with an ability to run profit for the firm. Harry added, "I run a tight ship around here and look for only one thing: your ability to add value to our bottom line. I don't like creative-types. Everything we do here has a purpose and is tried-and-true."

Fred and Amy, two junior associates, were assigned to Mike's account. Amy, a Harvard grad, had already made a name for herself by being aggressive with numbers. Fred, a UCLA grad, was reserved and liked to proceed methodically through a project. He wasn't like around the firm but was loyal to his partners.

Fred had consulted the Codes of Conduct and Code of Ethics on other accounts, and wanted to know on what issues these documents related on the Pfeifer account. The brothers and sisters are directors and officers charged with fiduciary duties in running the corporation. One of the directors, Sue, had recently purchased some property worth $25 million without getting permission from the board. Mike read a note on the memo that read, "Hide this purchase--Pfeifer doesn't want this transaction to show on financials. We don't want other clients to know about this--could negatively impact investment advice. H.S." Mike showed Amy and Fred this note. Fred objected, saying that the Codes prohibit hiding such information. Amy said it probably will never be discovered. Answer the following questions:

1. What options do Mike, Amy, and Fred have in terms of the note? In your answer, discuss issue management theories and strategic management approaches.

2. What ethical system(s) describes the corporate culture at SC&W? Is this an example of Immoral Management, Moral Management, or Amoral Management, according to Lynn Sharp Paine's models? Explain.

Over the years, large business organizations have steadily reduced the number of layers in the organization structure. What purposes has this profound change in structure served? If you were the CEO of a large organization, would you want to share responsibility with a co-CEO? Why or why not? What can first-level and middle-level managers and team leaders to about shaping the culture of a firm? What can you tell about the organizational culture of a large retailer just by visiting a couple of the firm's stores? How can a manager tell whether an employee is resisting change? Describe how a business person could be an effective manager yet an ineffective leader. How would a leader know whether a given subordinate, or group of subordinates, is trustworthy enough to be empowered? Suppose that you as a manager found out that Jennifer, one of your team members, has a strong intrinsic motivation. What would you do with this information to motivate Jennifer to higher levels of performance? Some managers object to systematic approaches to motivating employees by expressing the thought, "Why should we go out of our way to motivate workers to do what they are paid to do?" What is your reaction to this objection?

4. Suppose a doctor's visit actually costs $90. In other words, the marginal cost of seeing the doctor is constant at $90. Bob has demand for doctor's visits given by the following equation where is the quantity demanded and P is the price of a doctor's visit: = 100.5

e. Suppose Bob's insurance plan calls for a $50 co-pay. How many times will Bob go to the doctor? What is the dollar value of the moral hazard with the co-pay? Illustrate with a diagram and calculate.

f. Compare and contrast your analysis in part e. to the situation where the insurance company requires a 20% coinsurance rate instead of a co-pay.

g. Is it possible that the co-pay or coinsurance cold actually reduce social wellbeing? Explain

Give an example of a situation where applying the Pigouvian solution to an externality problem makes the outcome less efficient than doing nothing. Your example must be a numerical example where taxing is the inefficient or not the least-cost avoider solution.

3. Explain in your own words, Coase's critique of Pigou. [Note: Coase has two criticisms of Pigou's approach to negative externalities such as pollution].

4. What is the Pigouvian solution to negative externalities? How would Pigou deal with positive externalities? What are the difficulties in implementing the Pigouvian solution to externalities in general?

5. An airport has only one airline flying out of it; the land under the flight path belongs to ten landowners. The airline can either do nothing to reduce noise from planes landing and taking off, or spend a million dollars a year to completely eliminate the noise; for simplicity we assume that those are its only alternatives. The landowners can use the land either for housing or as a farmland. Each landowner's property is worth $200,000/year as a farmland; $400,000/year as a housing without airplane noise; $320,000/year as a housing with airplane noise. Suppose the transaction costs are very high, giving the same outcomes as (i) the airline is not liable for noise: (il) the airline is liable for noise, how large is the inefficiency from each rule, relative to the efficient outcome? (i) How large is the inefficiency relative to the efficient outcome when the airline is not liable for noise? (ill) How large is the inefficiency relative to the efficient outcome when the airline is liable for noise? (for this question, you need to elaborate and explain what could be the exception and to what extent this exception will the inefficiency vary)