PROBLEM (8) A risk averse decision maker with u(x) = square root(x) faces a lottery L that delivers $2500 or $100 with equal (1/2) probabilities. (a) Would he choose the lottery or a sure reward of $901 ? (b) Now suppose that he can buy “2 copies” of the lottery; this means there are 2 lotteries like above where the random prizes for each lottery is drawn independently with the probabilities above, and the sum reward from two lotteries is to be paid to the decision maker. Would the agent choose this “bundled lottery” or a sure reward of 2 x $901 = $1802 ? As you see, when the risk is independently replicated, the agent is less risk averse against aggregate risk that is composed of many “idiosyncratic risks”. PLEASE ANSWER ALL THE PART!

PROBLEM (8) A risk averse decision maker with u(x) = square root(x) faces a lottery L that delivers $2500 or $100 with equal (1/2) probabilities. (a) Would he choose the lottery or a sure reward of $901 ? (b) Now suppose that he can buy “2 copies” of the lottery; this means there are 2 lotteries like above where the random prizes for each lottery is drawn independently with the probabilities above, and the sum reward from two lotteries is to be paid to the decision maker. Would the agent choose this “bundled lottery” or a sure reward of 2 x $901 = $1802 ? As you see, when the risk is independently replicated, the agent is less risk averse against aggregate risk that is composed of many “idiosyncratic risks”. PLEASE ANSWER ALL THE PART!

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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You are playing a single joint game with all your fellow students where you have to choose an integer from (0,1,2, .100}. A player's payoff depends on the distance of his answer to 2/3 of the average of all players' answers; the closer the better. Example: Your answer is 45. There are two other players whose answers are 25 and 56. Then, the average is (45+25+56)/3=42. 2/3 of the average is 28. Your distance to 2/3 of the average is 145-28|=17. All players will be ranked according to their answer's proximity to 2/3 of the average. The top 25% of the players get 2 points. The next 50% get 1 point. The bottom 25% get 0 points. (In case of ties, points will be distributed evenly in the enlarged classes.) Please give your answer as a single integer from (0,1,2,3,.100}. A valid submission would look like this: 45
Bill and Chris are playing a game that involves a spinner. They have observed the following facts about the numbers on the spinner. (1) The four numbers on the spinner are equally likely. (2) They are all different and are positive integers. (3) The smallest number you can get with two spins of the spinner is 2, and the largest is 14. (4) The remaining numbers, when added together give 8. (5) It is impossible to get an odd number if you spin the spinner twice and add the results. Draw the spinner indicating the four numbers.
3. Use Monte Carlo simulation to simulate the sum of 100 rolls of a pair of fair dice.
(a)Consider a flight with a seating capacity of 160 seats. This flight is always full and there is a chance to be overbooked. The actual no-show rate (NSR) of the flight is 3.5% and the estimated NSR is 6.3%. If this flight is oversold according to the estimated NSR, what is the number of excess/extra passengers that will show up and there will be no seats for them on the day of departure? (b)Consider a flight with a seating capacity of 160 seats. This flight is always full and there is a chance to be overbooked. The actual no-show rate (NSR) of the flight is 3.5% and the estimated NSR is 6.3%. If the one-way fare of this flight is $300. If this flight is oversold according to the estimated NSR, what is the additional revenue that this flight will generate due to overbooking?
Imagine you have three coins: one is fair, one is biased (twice as likely to be heads as tails), the third is also biased (twice as likely to be tails as heads). You pick one of the three coins at random, and flip it 20 times. How should you decide which coin you are holding, based on the results, to maximize your probability of being correct?
The Harriet Hotel in downtown Boston has 100 rooms that rent for $150 per night. It costs the hotel $30 per room in variable costs (cleaning, bathroom items, etc.) each night a room is occupied. For each reservation accepted, there is a 5% chance that the guest will not arrive. If the hotel overbooks, it costs $200 to compensate guests whose reservations cannot be honored. How many reservations should the hotel accept if it wants to maximize the average daily profit?
Problem #1: EXAMPLE 4.13 It has been stated that about 41% of adult workers have a high school diploma but do not pursue any further education. If 20 adult workers are randomly selected, find the probability that at most 12 of them have a high school diploma but do not pursue any further education. How many adult workers do you expect to have a high school diploma but do not pursue any further education? Find P(xs 12).
Situation 2: I went to the grocery store and I noticed that there are five different kinds of brown sugar at different prices, each brand has different probabilities that they will be sold. What formula should I use if I want to determine how the prices vary from the average price of the product that would be sold to the customers repeatedly?
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.
PROBLEM (6) A farmer with expected utility preferences with u(x) = sqaure root(x) can experience a Bountiful or a Dry year with probabilities %80 and %20, and with $100 and $25 worth of crops, respectively. (a) Calculate the expected value and expected utility of the “lottery” the farmer is facing. What is the certainty equivalent and risk premium of this lottery for the farmer? (b) The farmer’s risk-neutral friend offers him the following “insurance” scheme: “Give me $B if the year is bountiful and I will compensate you with $D if the year is dry” What should the numbers B and D be so that the friend would be willing to offer such a scheme and the farmer would want to accept it? (Just write down the conditions, that is, the mathematical inequalities that B and D should satisfy; don’t try to solve these equations !) (c) For which set of (B,D) values: (i) (19,96) or (ii) (36,56) or (iii) (19,75) the friend would offer and the farmer would accept the scheme? (Plug the values into the…