5. Suppose that a life-table mortality pattern is as follows: from ages 20 through 60, twice as many lives die in each five-year period as in the previous five-year. Also, it is known that 5p20 = 0.99. Find the probability that a life aged 20 will die between ages 40 and 50.
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- It should be stated that the battery of a pos device has an exponential distribution with an average life span of five years in standard use. What is the probability that a user who uses a Pos device for 3 years without a battery problem will encounter a battery problem in the next year?Suppose that the time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with 1 = 0.0003. What proportion of the fans will last at most 10,000 hours? What proportion of the fans will last at least 7000 hours? a. 0.0498, 0.1225 O b.0.9502, 0.1225 O c. 0.0498, 0.8775 O d. NONEFind the probability that the total number of breakdowns that occur in a particular 4-week period is exactly 10, giving the answer to 4 decimal places.
- In a certain study, the chance of encountering a car crash on the road is stated as 20%. Express that as a probability (which means it should be written as a decimal or a reduced fraction.)As the number of cars a person owns increases, so does the life expectancy of the person. What is the most likely explanation? Wealth is the common underlying cause Having more cars causes people to live longer. It is a coincidence1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.
- suppose that on-the-job injuries in a textile mill occur at the rate of 0.1 per day. A, what is the probability that two accidents will occur during the next (five-day) work week? B, in the probability that four accidents will occur over the next two work weeks, the square of your answer to part (a) explain?In any given year a factory has a 10% probability of having a serious accident about every how Nagy years might the factory expect to have an accident?Suppose a large shipment of laptop computers contained 12% defectives. If a sample of size 286 is selected, what is the probability that the sample proportion will be less than 7% ? Round your answer to four decimal places.
- We state that the battery of a type of pos device shows an exponential distribution with an average life span of five years in standard use. What is the probability that a user who uses the POS device for three years without battery problem will encounter a battery problem within the next year?5. A pressure transducer regulates a climate control system in a factory. The transducer fails according to an exponential distribution with rate one failure every five years on average. a. What is the cumulative distribution function of the time until failure? b. What is the probability that a transducer chosen at random functions for eight years without failure? irteen Reliability and Maintainability c. What is the probability that a transducer that has functioned for eight years con- tinues to function for another eight years?According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately two per 1,000 babies in a healthy baby nursery. The number climbs to an average of 30 per 1,000 babies in an intensive care nursery. Suppose that 1,000 babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly two babies were born deaf. (Round your answer to four decimal places.)