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Unformatted text preview: of the previous problem but now suppose that the two tellers have exponential service times with rates µ. Again, answer questions (a), (b), and (c). 2.12. A ﬂashlight needs two batteries to be operational. You start with four batteries numbered 1 to 4. Whenever a battery fails it is replaced by the lowestnumbered working battery. Suppose that battery life is exponential with mean 100 hours. Let T be the time at which there is one working battery left and N be the number of the one battery that is still good. (a) Find ET . (b) Find the distribution of N . (c) Solve (a) and (b) for a general number of batteries. 2.13. A machine has two critically important parts and is subject to three di↵erent types of shocks. Shocks of type i occur at times of a Poisson process with rate i . Shocks of types 1 break part 1, those of type 2 break part 2, while those of type 3 break both parts. Let U and V be the failure times of the two parts. (a) Find P (U > s, V > t). (b) Find the distribution of U and the distribution of V . (c) Are U and V i...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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