In an automatic geolocation system, a dispatcher sends a

Chapter 8, Problem 8.23

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In an automatic geolocation system, a dispatcher sends a message to six trucks in a fleet asking their locations. The 'vaiting times for responses from the six trucks are iid exponential rando1n variables, each \Vith expected value 2 seconds. (a) What is the probability that all six responses will arrive within 5 seconds? (b) If the system has to locate all six vehicles within 3 seconds, it has to reduce the expected response time of each vehicle. \1Vhat is the maximum expected response time that will produce a location time for all six vehicles of 3 seconds or less \vith probability of at least 0.9?

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