aultable 1-year loans with a principal of $1 million each. The probability of default on each loan is 2.5%. Assume that if one loan defaults, t
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Consider two defaultable 1-year loans with a principal of $1 million each. The probability of default on each loan is 2.5%. Assume that if one loan defaults, the other does not. Assume that in the event of default, the loan leads to a loss that can take any value between $0 and $1 million with equal probability, i.e., the probability that the loss is higher than $ ? million is 1 − ?. If a loan does not default, it yields a profit equal to $20,000. Compute the 1-year 98% Value at Risk (VaR) and Expected Shortfall (ES) of a single loan.
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- 1. Suppose a manufacturer produces two types of products, A and B. The probability that a product is defective is 0.05 for product A and 0.03 for product B. The probability that a randomly selected product is type A is 0.6. Find the probability that a randomly selected product is defective and type B.Solve in R programming language: Suppose that the number of years that a used car will run before a major breakdown is exponentially distributed with an average of 0.25 major breakdowns per year. (a) If you buy a used car today, what is the probability that it will not have experienced a major breakdown after 4 years. (b) How long must a used car run before a major breakdown if it is in the top 25% of used cars with respect to breakdown time.If the company invests 100,000 USD or less, their profit will be based on 75,000 USD as first 25,000 USD goes to set up the business in the first place. For the first 100,000 USD, the profit margin is low: 4.5%. Therefore, for every 100 dollar they spend, they get a profit of 4.5 dollar. For an investment greater than 100,000 USD, for the first 100,000 USD (actually on 75,000 USD as 25,000 is the setup cost), the profit margin is 4.5% whereas for the rest, it goes up to 8%. For example, if they invest 250,000 USD, they will get an 8% profit for the 150,000 USD. In addition, from the rest 100,000 USD, 25,000 is the setup cost and there will be a 4.5% profit on the rest 75,000. The investment will always be greater or equal to 25,000 and multiple of 100. Complete the RECURSIVE methods below that take an array of integers (investments) and an iterator (always sets to ZERO(‘0’) when the method is initially called) and prints the profit for the corresponding investment. You must…
- The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been found to be 70 with a standard deviation of 9.5 Assume that the distribution is approximately normal. What is the probability that an elite athlete has a maximum oxygen uptake of 65 ml/kg or lower?A car rental agency at a local airport has available 5 Fords, 7 Chevrolets, 4 Dodges, 3 Datsuns, and 4 Toyotas. If the agency randomly selects 9 of these cars to chauffeur delegates from the airport to the downtown convention center, a. Find the probability that a Ford, a Chevrolets, 2 Dodges, 2 Datsun and 3 Toyotas are used.b. Find the probability that 2 Fords, 3 Chevrolets, 1 Dodge, 1 Datsun and 2 Toyotas are used. 4 decimal places pleaseA nine character long password is to be created using lower-case letters, four special characters {!, @, #, $} and digits. For the password to be valid, it must contain at least one lower-case letter, one of the given special characters and one digit. What is the probability that a randomly generated nine character password is valid? Assume that the password is generated using only the lower-case letters, the given special characters and digits
- At the beginning of each year, a firm observes its asset position (call it d) and may invest any amount x (0 <=x <=d) in a risky investment. During each year, the money invested doubles with probability p and is completely lost with probability 1 - p. Independently of this investment, the firm’s asset position increases by an amount y with probability qy (y may be negative). If the firm’s asset position is negative at the beginning of a year, it cannot invest any money during that year. The firm initially has $10,000 in assets and wants to maximize its expected asset position ten years from now. Formulate a dynamic programming recursion that will help accomplish this goal.A Company supplies a range of cosmetics products and gives discounts on orders as follows: For order worth less than kshs 1000 a discount of 2% is given. For orders worth kshs 1000 and above a discount of 5% is given. These discount are only given if the customer’s account is less than four weeks in arrears. If the account is more than eight weeks in arrears a pro forma invoice must be sent and settled before dispatch. a) Prepare a mixed entry decision table b) Convert the above (Question 1,A) to Pseudocodes c) Under what circumstances would a software engineer use Throw-Away prototyping Evolutionary protopypingAssuming all Ghanaians who are at least 18 years can choose between going to school or learning a trade. It takes four years to either complete school or learn a trade. GHC 100 is invested every month for a person who chooses to go to school by the government till the person attains age 30 years provided he/she completes university. If he/she does not complete university, the payment is stopped at the time he/she exited. If the person chooses to learn a trade, the government pays GHC 2000 as apprentice fee to the madam or master who will take the person as an apprentice, and invest GHC 70 a month till age 30 years. If the person does not complete the apprenticeship, the payment is stopped at the time he/she exited. Remember that persons who are less than 18 years or above 30 years do NOT qualify to enroll on this program. You are to write a java program for the above scenario. Your program should a) request a person’s name, age, what he/she wants to do (go to school or learn a…
- Bayes’ Rule John is holding an outdoor party on Saturday. In recent years, on average it has rained36.5 days each year. When it rains, the weatherman correctly forecasts rain 80% of thetime. When it doesn't rain, the weatherman incorrectly forecasts rain 20% of the time.The weatherman predicts rain for Saturday. Using the Bayes’ theorem defined in Equation(1), what is the probability that it will rain on Saturday?List the steps to calculate each item in Equation (1). ?(??|?) =?(?|??)×?(??) / ∑ ?(?|??)×?(??)Equation (1)In a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet. Indicate the causal relationships in this system with arrows and signs. Show the causality loops in this system, at least 1 negative, at least 1 positive, and…In a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet.