An insurance company has a life insurance policy, which have 10,000 clients, each client pays 200 yuan per year. If the client died in this year, the company paid out the beneficiary of 10,000 yuan. The mortality rate for the client is 0.017 , and what is the probability of the insurance company will deficit in this year?
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An insurance company has a life insurance policy, which have 10,000 clients, each client pays 200 yuan per year. If the client died in this year, the company paid out the beneficiary of 10,000 yuan. The mortality rate for the client is 0.017 , and what is the probability of the insurance company will deficit in this year?
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- At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.The number of hybrid cars that have be requested for rental from a car rental office during a 50 day sample period is given in the following table. Demand for Cars Number of Days Probability 3 3 0.06 4 7 0.14 5 12 0.24 6 14 0.28 7 10 0.20 8 4 0.08 50 1.00What is the expected (mean) number of hybrid rentals per day? Compute to one decimal place.7. Assume that there is a 9% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? a. With two hard disk drives, the probability that catastrophe can be avoided is nothing. (Round to four decimal places as needed.)
- A factory has a frequency of breakdown of their machine per month as shown in table below and the cost of breakdown remains the same but the cost of preventive maintenance becomes ksh 1250 per month, and given that if preventive maintenance is performed, probability of a machine breakdown is negligible. Determine whether the engineer should use preventive maintenance or would it be cheaper to repair the machine when it breakdown. Frequency of breakdown of machine per month Number of breakdown 0 1 2 3 Frequency 20 30 40 10A hospital has three independent fire alarm systems, with reliabilities of .95, .97, and .99. In the event of a fire, what is the probability that a warning would be given?7. A piece of equipment has a lifetime T (measured in years) that is a continuous ran- dom variable with cumulative distribution function F(t) = 1 – e/10 – (1/10) e¯/10 for all t> 0. a. What is the probability density function of T? b. What is the probability that a piece of equipment survives more than 20 years? c. What is the probability that a piece of equipment survives more than 10 years but fewer than 20 years? d. What is the probability that a piece of equipment survives more than 20 years given that it has survived for 10 years? 8. For the equipment mentioned in Problem 7, a. Derive the failure rate function r(1), and draw a graph of the function. b. Without using the failure rate function, determine the probability that a piece of equipment that has survived 20 years of operation fails in the 21st year. c. Does r(20) accurately estimate your answer to part (b)? Why or why not?
- An expensive piece of equipment is used in the masking operation for semiconductor manufacture.A capacitor in the equipment fails randomly. The capacitor costs $7.50, but if it burns out while the machine is in use, the production process must be halted. Here the replacement cost is estimated to be $150. Based on past experience, the lifetime distribution of the capacitor is estimated to be Number of Months Probability of of Service Failure 1 .08 2 .12 3 .16 4 .26 5 .22 6…Using the basic risk management matrix, explain the following: a. When would you buy insurance? b. When would you avoid the risk? c. When would you retain the risk? d. When would you use loss control?An expensive piece of equipment is used in the masking operation for semi-conductor manufacture. A capacitor in the equipment fails randomly. The capacitor cost $7.50, but if it burns out while the machine is in use, the production process must be halted. Here the replacement cost is estimated to be $150. Based on past experience, the lifetime distribution of the capacitor is estimated to be Number of Months of Service 1 2 3 4 5 6 Probability of Failure 0.08 0.12 0.16 0.26 0.22 0.16 How often should the capacitors be replaced in order to minimize the expected monthly cost of planned and unplanned replacement?
- 4. From past experience, Anna knows that the probability that her friend will take her to dinner in Orro Resto id 0.7, the probability that they will watch movies is 0.5, and the probability that he will take her to dinner or they will watch movies is 0.9. What is the probability that they will do both? they will do neither? 5. Eight persons enter a supermarket. From the past experience, it is known that 25% of the people entering the supermarket make a purchase. What is the possible values of the random variable X? Construct the probability distribution of X. X P(X=x) What is the probability that 1) at least four persons will make a purchase? 2) two or three persons will make a purchase? 3) a most two persons will make a purchase?Classify the following risks into variation, foreseen uncertainty, unforeseen uncertainty, and chaos:d. A cool summer causes a decrease in demand for air conditioners for that seasonA national survey indicated that 30% of adults conduct their banking online. It also found that 40% are under the age of 50, and that 25% are under the age of 50 and conduct their banking online. A. What is the probability that an individual conducts banking online given that the individual is under the age of 50? B. Are Banking Online and Age independent? Explain.