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Chapter 8: Q 8.4 (page 390)
Let X1, ... , X20 be independent Poisson random variables with mean 1.
(a) Use the Markov inequality to obtain a bound on
(b) Use the central limit theorem to approximate
a)
b)
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A person has 100 light bulbs whose lifetimes are independent exponentials with mean 5 hours. If the bulbs are used one at a time, with a failed bulb being replaced immediately by a new one, approximate the probability that there is still a working bulb after 525 hours.
A.J. has jobs that she must do in sequence, with the times required to do each of these jobs being independent random variables with a mean ofminutes and a standard deviation ofminutes. M.J. has jobs that he must do in sequence, with the times required to do each of these jobs being independent random variables with a mean ofminutes and a standard deviation of minutes.
Find the probability that A.J. finishes in less than minutes.
Find the probability that M.J. finishes in less thanminutes.
Find the probability that A.J. finishes before M.J.
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Suppose in Problem that the variance of the number of automobiles sold weekly is.
Give a lower bound to the probability that next week鈥檚 sales are between and, inclusively.
Give an upper bound to the probability that next week鈥檚 sales exceed.
8.6 . In Self-Test Problem , how many components would one need to have on hand to be approximately percent certain that the stock would last at least days?
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