Consider a betting system with two possible outcomes labelled 1 and 2, and two possible wagers, also labelled 1 and 2. The returnfunction is given by r₁ (1) = 2.4, r₁ (2) = 3.3, r₁ (2) = x, and r₂(2) = 0.7, where x is a real number. You are told that the bettingsystem is fair, that is, there is no arbitrage. Determine x correct to 3 significant digits.Answer:

Step 1: Set Up Fairness Equations Step 2: Solve for x Using p1

Answered: Consider a betting system with two…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Given P(A) = 0.21, P(B) = 0.24, and P(B|A) = 0.24, are A and B independent or dependent?
Avicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences property damage in the next five years, the company must pay out $23,600 to the policy holder. Executives at Avicenna are considering offering these policies for $791 each. Suppose that for each holder of a policy there is a 3% chance they will experience property damage in the next five years and a 97% chance they will not. (If necessary, consult a list of formulas.) If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much? To answer, take into account the price of the policy and the expected value of the amount paid out to the holder. O Avicenna can expect to make money from offering these policies. In the long run, they should expect to make dollars on each policy sold. O Avicenna can expect to lose money from offering these policies.…
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Rhett owns a cupcake bakery and is analyzing his sales of cupcake delivery orders. Based on his daily sales of delivery orders for the past month, he has already calculated the probabilities, ?(?),P(X), for the number of boxes of cupcakes, ?,X, purchased by a single customer in a single day, as shown in the table. ?X 1 2 3 4 5 ?(?)P(X) 0.75 0.05 0.10 0.05 0.05 Calculate the mean number of boxes of cupcakes, ??,μX, sold and delivered per person in a single day. Express your answer to two decimal places. ??=μX= If a box of cupcakes costs $40.00$40.00 and the flat-rate delivery fee is $7.00$7.00, calculate the mean sales per person, ??,μY, that the cupcake shop makes in a single day for delivery orders. Express your answer to the nearest cent. ??=$μY=$
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Suppose a person is thinking about entering a MarioKart competition at theirlocal videogame store. The competition costs 20 dollars to enter. The competition consists of 10 matches. The person knows that their chance of winning each match is 65% and that each match is independent of the others. The payout for the competition is: WIN ALL 10 Matches: 500 Dollar Prize WIN 9 Matches: 250 Dollar PrizeWIN 8 Matches: 50 Dollar Prize OTHERWISE: Nothing 1) Suppose that this person enters the competition 5 times.What is the probability they break even?(Hint: To break even they would need to win the $50 prize twice and lose the other three times. Use a modified binomial to calculate this probability.)
A fast food company is offering a prize promotion game. The company claims that in 0.5 % 0.5% of all orders will receive $ 100 $100 cash, 1 % 1% of all orders will receive $ 10 $10 cash, and 10 % 10% of orders will receive a coupon for a free soft drink. The remaining orders will receive no prizes. A group of long-time customers were excited about the new promotion, and over the course of the promotion, they placed 651 orders 651 orders. Of these orders, 2 2 ended up winning $ 100 $100, 6 6 won $ 10 $10, and 52 52 won a free soft drink. The group wants to do a chi-squared goodness of fit test to test the advertised odds. Are the conditions met for this test?
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You consider buying insurance for your car for the next year. Your car is worth £15000. Historical data shows that you have 85% chance of not having any accident next year, 12% chance of having a minor accident, and 3% chance of having a serious accident, destroying the car. [For moral purposes, we assume your physical integrity not to be diminished, only the car is affected, not the persons inside]. The insurance company will pay the cost of the damage, which is estimated on average at £5000 for a minor accident, and of course the value of the car if it is destroyed. You adopt a risk-averse approach, with utility function U(x)=log(x+1000). We consider the insurance company to be risk-neutral. The cost of the insurance is £k. For which values of k (rounded) are both parties (you and the insurance company) happy to trade?
Two people A and B play a series of games, in which they bet on a particular share price increasing or decreasing on a particular day. If the share price increases, player B pays player A £1; whereas if the share price decreases, player A pays player B £1. The probability of the share price increasing on any particular day is p independently of any other day, and the probability of the share price decreasing is q = (1– p). Initially, both A and B have £2, and the series of games ends when one player runs out of money. We let X, be amount of money possessed by player A after n days, so Xo = 2, and we consider the random process Xo, X1, X2, .... (a) Explain why the state space of this random process is {0, 1, 2, 3, 4}. (b) Explain why this random process is a Markov process. (c) Explain why the transition matrix for this random process is 1 0 0 0 0 q 0 p 0 0 0 0 q 0 p 0 0 0 0 1 (d) What is the 2-step transition matrix for this Markov process? (e) Classify the states of this random…
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