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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A risk averse individual faces uncertainty with two outcomes: good, bad. Theindividual has income $1260 at good and $840 at bad outcome. The probability of good outcome is 5/7 (so the probability of bad outcome is 1 – 5/7 = 2/7). The individual can buy any nonnegative x units of insurance. Every unit of insurance has price $p and it pays $1 in the event of bad outcome. In this insurance market, the unit price of insurance is known to be p = 2/3. (a)Suppose the individual buys x units of insurance. Determine the individual's net income under good income, net income under bad income and the average net income. Draw these three in a diagram as functions of x. (b) For the individual: (i) compare full insurance with over insurance and (ii) compare full insurance with partial insurance. Then determine best choice of insurance for the individual.
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?
You are applying for a job at two companies. Company A offers starting salaries with μ=$34,000 and σ=$1,000. Company B offers starting salaries with μ=$34,000 and σ=$3,000. From which company are you more likely to get an offer of $36,000 or more?
Mr. Adams and Ms. Smith are betting on repeatedflips of a coin. At the start of the game Mr. Adams hasa dollars and Ms. Smith has b dollars, at each flip the loser pays the winner one dollar, and the game contin-ues until either player is “ruined.” Making use of the fact that in an equitable game each player’s mathematicalexpectation is zero, find the probability that Mr. Adamswill win Ms. Smith’s b dollars before he loses his adollars.
If P(A) = .85, P(B) = .76, and P(A ∩ B) = .72, then P(A | B) =
1. Mindy is taking MA 385 this summer and two sections are offered. She estimates that if she takes Dr. J, her chance of passing the course is 80%, but if she takes Dr. S, her chance of passing the course is only 60%. There is a 40% chance she will get in Dr. J's class, otherwise she will be placed in Dr. S's class. After the summer is over, you learn that Mindy passed MA 385. What is the probability that she was enrolled in Dr. J's section?
Possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities 0.35, 0.15, 0.35, and 0.15, respectively. (a) Calculate E(X) and then E(5 - X). E(X) E(5-X) = (b) Would the repair facility be better off charging a flat fee of $70 or else the amount $ 150 (5-X) The repair facility ---Select--- be better off charging a flat fee of $70 because E ]= 150 (5-X)] ? Note: It is not generally true that : E ( =) = E(Y)
A charity organization is selling $50 raffle tickets as part of a fund-raising program. The grand prize is a trip to Mexico valued at $12750, and the runner-up prize is a weekend spa package valued at $1500. Twenty other players will receive $250 gift cards for a local grocery store. The organization will sell a total of 4500 tickets, and the winners will be selected via random drawing. Let x = net winnings earned from buying one ticket for this raffle (i.e. x = ticket winnings - ticket cost) a) Write a valid probability distribution (in table format) for x. Make sure you consider ALL of the possible outcomes associated with buying a ticket. X P(x) b) Use your distribution to determine the EXPECTED VALUE associated with buying a single raffle ticket. Show valid supporting work! time you
An amount of $10,000 is to be invested for three years. The yield rate for the first year will be equally likely to be 5%, 6%, 7%, 8% or 9%; for the second year will be equally likely to be 7% or 9%; for the third year will be 7%, 8% or 9% with probabilities 0.3, 0.5 and 0.2, respectively. The yield rates in different years are independent. Find the probability that the accumulation of the investment for the three years will be greater than its expected value.
For this problem, assume that you have 4 outcomes, and that you know the following about them: w2=0.15w2=0.15, w4=0.25w4=0.25, and w1=w3w1=w3. What is the value of w1w1?
Options: A. The odds of working for men are 0.62 B. the odds of working are 0.62 times as large among men compared to women C. the odds of working are 0.62 times as large women compared to men D. the odd of working for women are 0.62
You are analyzing stocks of three companies you are interested in investing in. Suppose that these three stocks are Apple stock (AAPL), Microsoft (MSFT), and Tesla (TSLA). At the end of this month, each month may move up (increase in value), move down (decrease in value) or stay the same. In this case, an experiment consists of observing the price condition across the three stocks. Each of the three conditions (move up, move down, stay same) are equally likely. How many outcomes are in the sample space? List 7 of the outcomes. (use U for move up, D for moving down and S for staying the same) Let A be the event that all the stocks have the same performance. List the outcomes in A. Let B be the event that all of stocks are different. List the outcomes in B. Let C be the event that at least two stocks move up. Are events A and C mutually exclusive? Are events B and C mutually exclusive? What is the probability of ? What is the probability of ? What is the probability of ? What is the…

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