We have 100 components that we will put in use in a sequential fashion. That is, component 1 is initially put in use, and upon failure, it is replaced by component 2, which is itself replaced upon failure by component 3, and so on. If the lifetime of component i is exponentially distributed with mean 10 + i/10, i = 1, . . . , 100, estimate the probability that the total life of all components will exceed 1200. Now repeat when the life distribution of component i is uniformly distributed over (0, 20 + i/5), i = 1, . . . , 100.
Answer to relevant QuestionsStudent scores on exams given by a certain instructor have mean 74 and standard deviation 14. This instructor is about to give two exams, one to a class of size 25 and the other to a class of size 64. (a) Approximate the ...Let X be a nonnegative random variable. Prove that E[X] ≤ (E[X2])1/2 ≤ (E[X3])1/3 ≤ . . . In Problem 7, suppose that it takes a random time, uniformly distributed over (0, .5), to replace a failed bulb. Approximate the probability that all bulbs have failed by time 550. Problem 7 A person has 100 light bulbs ...On any given day, Buffy is either cheerful (c), so-so (s), or gloomy (g). If she is cheerful today, then she will be c, s, or g tomorrow with respective probabilities .7, .2, and .1. If she is so-so today, then she will be ...Use the inverse transformation method to present an approach for generating a random variable from the Weibull distribution
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