a) A dealer decides to sell an antique automobile by means of an English auction with areservation price of £900. There are two bidders. The dealer believes that there are onlythree possible values, £7,200, £3,600, and £900, that each bidder's willingness to paymight take. Each bidder has a probability of 1/3 of having each of these willingnessesto pay, and the probabilities for each of the two bidders are independent of the other'svaluation. Assuming that the two bidders bid rationally and do not collude, the dealer'sexpected revenue from selling the car is at leastb) A seller knows that there are two bidders for the object she is selling. She believes thatwith probability 1/2, one has a buyer value of £5 and the other has a buyer value of £10and, with probability 1/2, one has a buyer value of £8 and the other has a buyer valueof £15. She knows that bidders will want to buy the object so long as they can get it fortheir buyer value or less. She sells it in an English auction with a reserve price whichshe must set before the auction starts. To maximize her expected profits, she should setthe reserve price at what price?c) Portsmouth Bank has foreclosed on a home mortgage and is selling the house at auction.There are three bidders for the house, Emily, Anna, and Olga. Portsmouth Bank doesnot know the willingness to pay of these three bidders for the house, but onits previous experience, the bank believes that each of these bidders has a probabilityof 1/3 of valuing it at £600,000, a probability of 1/3 of valuing at £500,000, and aprobability of 1/3 of valuing it at £200,000. Portsmouth Bank believes that theseprobabilities are in de pendent among buyers. If Portsmouth Bank sells the house bymeans of a second- bidder, sealed- bid auction (Vickrey auction), what will be thebank's expected revenue from the sale?the basis of

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Answered: a) A dealer decides to sell an antique…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of $1,425,000 if successful and a yearly loss of $475,000 otherwise. The probability of success is 1. If the second mall is selected, it is estimated that the yearly profit will be $950,000 if successful; 3 otherwise, the annual loss will be $285,000. The probability of success at the second mall is Complete parts (a) through (c) below 4 - a. What is the expected profit for the first mall?
In a town, there are three bridges: Bridge A, Bridge B, and Bridge C. On any given day, the probability of each bridge being open for passage is as follows: P(A) = 0.4, P(B) = 0.3, and P(C) = 0.5. If a resident needs to cross all three bridges in succession, what is the probability of successfully crossing all three bridges without encountering any closures?
The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 30% chance it will be bad. If the weather is indifferent today, there is a 50% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. a. What is the stochastic matrix, P, for this situation? b. Suppose there is a 10% chance of good weather today and a 90% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 40% indifferent weather and 60% bad weather. What are the chances for good weather on Wednesday? a. Create the stochastic matrix, P, where G is good, I is indifferent, and B is Bad. From: GIB a (Simplify your answers.) To: G
Your probability professor has a tabby cat who sleeps 34% of the time and seems to respond to stimuli more or less randomly. If a human pets her when she’s awake, she will request more petting 8% of the time, food 38% of the time, and a game of fetch the rest of the time. If a human pets her when she’s asleep, she will request more petting 33% of the time, food 41% of the time, and a game of fetch the rest of the time. (You can assume that the humans don’t pet her disproportionally often when she’s awake.) • If the cat requests food when petted, what is the probability that she was asleep? • If the cat requests a game of fetch when petted, what is the probability that she was not asleep?
A retailer of automobile parts has four employees, K, L, M, and N, who make mistakes in filling an order one time in 100, four times in 100, two times in 100, and six times in 100. Of all the orders filled, K , L, M, and N fill, respectively, 20%, 40%, 30%, and 10%. If a mistake is found in a particular order, what are the probabilities that it was filled by K, L, M, or N?
In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly diagnosis 95% of all persons with diabetes as having the disease and incorrectly diagnoses ten percent of all persons without diabetes as having the disease, find the probabilities that: The health service will diagnose an adult over age 50 as having diabetes. A person over 50 diagnosed by the health service as having diabetes actually has the disease.
7. A drawer contains 6 black socks, 4 brown socks, and 2 green socks. Suppose one sock is drawn from the drawer and that it is equally likely that any one of the socks is drawn. Find the probabilities for each of the following: a. The sock is brown b. The sock is either black or green c. The sock is red d. The sock is not black
From a large survey of customers using a chain of coffee shops, 60% of the customers are male, 50% purchase food, 15% are both Male and purchase food. What are the probabilities that: A customer is both female and purchases food? A female customer purchases food? A customer purchasing food is female?
On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate. b sketch a tree diagram to model this process
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