1) Consider the joint pdf of the two components in Problem 1, and assume that they work as a serial subsystem, i.e. the subsystem consisting of the two components fails if at least one component fails.a. Find the reliability function for this subsystem (i.e. 1- F(t) ), where F(t) is the cdf of the time to failure of this subsystem.b. Find the expected value of the time to failure of the subsystem.c. Find the probability that the system failure is caused by the second component.2) Suppose that when an electronic component of a certain type is subjected to an accelerated life test, the lifetime X (in weeks) has a gamma distribution with mean 24 weeks and standard deviation 12 weeks.a. What is the probability that a component will last at least 30 weeks?b. What is the probability that a component will last between 12 and 30 weeks?c. Is the median of the lifetime distribution less than 24? Why or why not?3) Suppose that a company wishes to hire two new workers and that each applicant interviewed has a probability of 0.5 of being found acceptable.a. Find the probability that the total number of applicants the company needs to interview will exceed 5.b. Find the expected number of applicants the company needs to interview to hire two new workers.4) A company’s toll-free complaints line receives on average 40 calls per 8 hours. Use the Poisson distribution to estimate the following: a. The probability that in one hour there are at least 4 calls.b. Expected number of calls per hour.
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