An individual has a utility function U(W)= √w. where W is the level of wealth.They have been offered a gamble with a payout of 100 with a probability of 0.31 and a payout of £35 with a probabiity of 1-031.The Certainty Equivalent of this gamble is:
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An individual has a utility function U(W)= √w. where W is the level of wealth.They have been offered a gamble with a payout of 100 with a probability of 0.31 and a payout of £35 with a probabiity of 1-031.The Certainty Equivalent of this gamble is:
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- Managers of the restaurant, NicePizzeria@Nola, have to plan for the number of pizzas they want to make at the beginning of each day. Based on market research, the managers know the daily demand can only be one of the three levels: 30, 40 or 50 pizzas. Also, the probabilities of getting a daily demand of 30, 40, 50 pizzas are 0.3, 0.4, 0.3 respectively. The managers decide that their tentative daily supply of pizza should also be one of the three levels: 30, 40 or 50 pizzas. Each pizza costs $3 to make and the price is $8 per pizza. Note: The profit for each pizza sold is $5. For the ones supplied but not sold, the profit is -$3. Fill in the following profit table (hint: use two-way table ) and use the profit table to answer the questions. Three demand levels 30 40 50 30 Three supply 40 levels 50 1) What is the maximin supply level? 2) What is the maximum expected profit (across three supply levels)?A software developer makes 175 phone calls to its current customers. There is an 8 percent chance of reaching a given customer (instead of a busy signal, no answer, or answering machine). The normal approximation of the probability of reaching at least 20 customers is Multiple Choice .022 .007 .063 .937Suppose A and B are two events with probabilities: P(A) = .30, P(B°) = .45, P(AN B) = .15. Find the following: а) Р(A U B). b) Р (4°). с) Р(B).
- Problem 1. A new edition of a very popular textbook will be published a year from now. The publisher currently has 2000 copies on hand and is deciding whether to do another printing before the new edition comes out. The publisher estimates that demand for the book during the next year is governed by the probability distribution on the image . A production run incurs a fixed cost of $10,000 plus a variable cost of $15 per book printed. Books are sold for $130 per book. Any demand that cannot be met incurs a penalty cost of $20 per book, due to loss of goodwill. Up to 500 of any leftover books can be sold to Barnes & Noble for $35 per book. The publisher is interested in maximizing expected profit. The following print- run sizes are under consideration: 0 (no production run) to 16,000 in increments of 2000. What decision would you recommend? Use simulation with 1000 replications. For your optimal decision, the publisher can be 90% certain that the actual profit associated with…The time taken to complete a bicycle race is normally distributed, with anaverage time (μ) of 2.25 hours and a standard deviation (σ) of 0.65 hours.What is the probability that a randomly selected cyclist will: Q.7.3.1 Take between 2.75 and 3.15 hours to complete the race? Interpretyour answer. Q.7.3.2 Take between 2.05 and 2.15 hours to complete the race? Interpretyour answer.The closing price of Martin's Sporting Goods Inc. common stock is uniformly distributed between $25 and $36 per share. What is the probability that the stock price will be more than $32?
- 2.4 The opening 2018 World Cup odds against being the winning team specified by espn.com were 9/2 for Germany, 5/1 for Brazil, 11/2 for France, 20/1 for England, and 7/1 for Spain. Find the corresponding prior probabilities of winning for these five teams.The investor is considering how to optimally invest 1000 euros in stocks and bonds. Let's assume that the optimal decision is made based on expected utility. Suppose the investor has a utility function u(x)=ln(1+x), where x is their wealth. Let y be the proportion invested in stocks and 1−y be the proportion invested in bonds. By investing in stocks, the investor earns 1% with a probability of 39.5% and 4% with a probability of 60.5%. By investing in bonds, the investor earns a certain 2.8%. What proportion of the investment will the investor allocate to stocks and what proportion to bonds?An expected utility maximiser owns a car worth £60000£60000 and has a bank account with £20000£20000. The money in the bank is safe, but there is a 50%50% probability that the car will be stolen. The utility of wealth for the agent is u(y)=ln(y)u(y)=ln(y) and they have no other assets. A risk-neutral insurance company is willing to insure the car at the premium of π=£2/3π=£2/3 for every one pound of coverage. How much insurance coverage will the individual choose to buy? a. £30,000 b.£40,000 c. £80,000 d.£60,000
- A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed. f(x) = 7 for æ = 1,2, or 3 6 %3D %3D a. Consider the required conditions for a discrete probability function, shown below. f(x) > 0 (5.1) Ef(x) = 1 (5.2) Does this probability distribution satisfy equation (5.1)? - Select your answer- Does this probability distribution satisfy equation (5.2)? - Select your answer - b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)? c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)?An author is trying to choose between two publishing companies that are competing for the marketing rights to her new novel. Company A has offered the author $10,000 plus $2 per book sold. Company B has offered the author $2,000 plus $4 per book sold. The author believes that four levels of demand for the book are possible are: 1,000, 2,000, 3000 and 5000 books are sold. If the probabilities of each level of demand are as follows: Demand Probability 1000 0.31 2000 0.32 3000 0.25 5000 0.12 Construct the payoff table for each level of demand for company X and company Y. What are the expected monetary value (EMV) and expected opportunity loss (EOL)? Hence determine the best decision that this author should do.University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A student advisor needs to know the probability a newly admitted student is interested in such a program, so that the student can be properly advised. A study of previous years finds that the probability a student gets a Bachelor of Science degree is P(Science) = 0.3 and the probability a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The study also shows that the probability a student gets no degree is P(no) = 0.2. Some probability calculations show the probability of getting a Bachelor of Arts and Science degree to be P(Arts & Science) = 0.1. Getting a Bachelor of Arts degree and getting a Bachelor of Science degree are not independent because: P(Arts & Science) = P(Arts) P(Arts & Science) = P(Arts) P(Science) P(Arts & Science) = P(Arts |…