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- Find the expectation of obtainig a 4 upwards with 3 throws of a dice.A certain Mobile Money Agency is an agent for Zanaco Express, Airtel, MTN and Zamtel Mobile Money. Experience has shown that the probabilities of finding a float for withdrawals of amounts K5000 and above are given as 0.4, 0.5, 0.3 and 0.2, respectively. Experience has also shown that among his clients, the probabilities that a client requires a service from Zanaco Express, Airtel, MTN, Zamtel Mobile Money are given as 0.3, 0.4, 0.2 and 0.1, respectively. Assume that each client visits the agency for withdrawals from only one at a time.(i) What is the probability that a client who wishes to withdraw K5000 will not be successful?(ii) What is the probability that an MTN client who wishes to withdraw K5000 will not be successful?(iii) What is the probability that an Airtel client who wishes to withdraw K5000 will not be successful?(iv) A certain client has just failed to make a withdrawal of K7000, what is the probability that he/she is a Zamtel Mobile money client?Find the expectation and varience of X.
- A company is considering whether to market a newproduct. Assume, for simplicity, that if this product ismarketed, there are only two possible outcomes: successor failure. The company assesses that the probabilitiesof these two outcomes are p and 1 2 p, respectively. Ifthe product is marketed and it proves to be a failure, thecompany will have a net loss of $450,000. If the productis marketed and it proves to be a success, the company will have a net gain of $750,000. If the companydecides not to market the product, there is no gain orloss. The company can first survey prospective buyersof this new product. The results of the consumer surveycan be classified as favorable, neutral, or unfavorable.Based on similar surveys for previous products, thecompany assesses the probabilities of favorable, neutral,and unfavorable survey results to be 0.6, 0.3, and 0.1for a product that will eventually be a success, and itassesses these probabilities to be 0.1, 0.2, and 0.7 for aproduct that will…The ABC Co. is considering a new consumer product. They believe there is a probability of 0.4 that the XYZ Co. will come out with a competitive product. If ABC adds an assembly line for the product and XYZ does not follow with a competitive product, their expected profit is $40,000; if they add an assembly line and XYZ does follow, they still expect a $10,000 profit. If ABC adds a new plant addition and XYZ does not produce a competitive product, they expect a profit of $600,000; if XYZ does compete for this market, ABC expects a loss of $100,000. calculate the EVPIAssume that in a lake there are 15000 fish, 1000 of them marked [with radioactive tracers]. 150 fish were fished out of the lake. Find the expectation of the number of marked fish among the fish caught.
- At an electronics plant, it is known from past expe-rience that the probability is 0.84 that a new worker who has attended the company’s training program will meet the production quota, and that the corresponding prob-ability is 0.49 for a new worker who has not attended the company’s training program. If 70 percent of all new workers attend the training program, what is the proba-bility that a new worker will meet the production quota?An inspector is looking for nonconforming welds in the gasoline pipeline between Phoenix and Tucson. The probability that any particular weld will be defective is 0.01. The inspector is determined to keep working until finding three defective welds. If the welds are located 100 feet apart, what is the proba- bility that the inspector will have to walk 5000 feet? What is the probability that the inspector will have to walk more than 5000 feet?There is a 30% chance that any current client of company A will switch to company B this year. There is a 20% chance that any client of company B will switch to company A this year. If these probabilities are stable over the years, and if company A has 1000 clients and company B has 1000 clients, in the long run (assuming the probabilities do not change), what will the market shares be? For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
- Q5: There are 1% probability for a hard drive to crash. Therefore, it has two backups and each having 2% probability to crash, and all three components are independent of each other. Thestored information is lost only in an unfortunate situation when all three devices crash. What is the probability that information is saved?A game is fair when each player's expectation equates to zero. If we are paid ten dollars each time the sum of two tossed dice is greater than four, what should we pay in return each time the sum does not exceed four to make the game fair?A zero-coupon bond promises to pay $1000 in three years. However, there is a 20% probability that the bond issuer defaults and investors are only able to get $700. There is a further 10% probability that the bond issuer defaults and investors get nothing ($0). To clarify, there is a 70% probability that the bond pays off the full $1000 and a 30% total probability that the bond defaults and the investors get less than $1000. Assume that investors are risk neutral and that time-equivalent treasuries offer an interest rate of 8% per year. The bond is zero-coupon, so makes no intermediate payments. Part 1 What is the expected payoff (in dollars) of the bond in three years? Part 2 What is the current traded price of the bond today? (Remember that the bond pays off or defaults in three years.)