In an automatic geolocation system, a dispatcher sends a message to six trucks in a fleet asking their locations. The waiting times for responses from the six trucks are iid exponential random variables, each with 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 thime of each vehicle. What is the maximum expected response time that will produce a location time for all six vehicles of 3 seconds or less with probaility of at least 0.9?

In an automatic geolocation system, a dispatcher sends a message to six trucks in a fleet asking their locations. The waiting times for responses from the six trucks are iid exponential random variables, each with 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 thime of each vehicle. What is the maximum expected response time that will produce a location time for all six vehicles of 3 seconds or less with probaility of at least 0.9?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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