Bus Route "A", with headways of 10 minutes, and Bus Route "B", with headways of 20 minutes, merge along a common route with the headway sequence of 5 min, 5 min, 10 min, 5 min, 5 min, 10 min, ... A passenger who wishes to travel along the common route (i.e., she's willing to take a bus from either route "A" or "B") arrives at a random time. Determine: a) the probability that the passenger must wait less than a time W for the next arriving bus (i.e., define and sketch the CDF for waiting time); b) the probability that the passenger waits between 4 to 7 minutes for the next bus; c) the passenger's expected waiting time; and d) the probability that the first bus to arrive is from Route "B."
Bus Route "A", with headways of 10 minutes, and Bus Route "B", with headways of 20 minutes, merge along a common route with the headway sequence of 5 min, 5 min, 10 min, 5 min, 5 min, 10 min, ... A passenger who wishes to travel along the common route (i.e., she's willing to take a bus from either route "A" or "B") arrives at a random time. Determine: a) the probability that the passenger must wait less than a time W for the next arriving bus (i.e., define and sketch the CDF for waiting time); b) the probability that the passenger waits between 4 to 7 minutes for the next bus; c) the passenger's expected waiting time; and d) the probability that the first bus to arrive is from Route "B."
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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Bus Route "A", with headways of 10 minutes, and Bus Route "B", with headways of 20 minutes, merge along a common route with the headway sequence of 5 min, 5 min, 10 min, 5 min, 5 min, 10 min, ... A passenger who wishes to travel along the common route (i.e., she's willing to take a bus from either route "A" or "B") arrives at a random time.
Determine:
a) the
(i.e., define and sketch the CDF for waiting time);
b) the probability that the passenger waits between 4 to 7 minutes for the next bus;
c) the passenger's expected waiting time; and
d) the probability that the first bus to arrive is from Route "B."
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