A truck driver is waiting to join the traffic on the service road of a highway. The truck driver blocks the service road for four seconds when he joins the traffic. Suppose that vehicles arrive according to a Poisson process and that six seconds elapse, on average, between two consecutive vehicles. Answer the following questions by assuming that the truck driver makes sure that he has enough time to perform his maneuver before merging into the traffic. (a) What is the probability that the truck driver is able to join the traffic immediately on his arrival at the intersection with the service road? (b) What is the mathematical expectation of the gap (in seconds) between the truck and the nearest vehicle when the truck driver merges into the traffic? (c) Calculate the average number of vehicles that the truck driver must let go by before being able to merge into the traffic.
A truck driver is waiting to join the traffic on the service road of a highway. The truck driver blocks the service road for four seconds when he joins the traffic. Suppose that vehicles arrive according to a Poisson process and that six seconds elapse, on average, between two consecutive vehicles. Answer the following questions by assuming that the truck driver makes sure that he has enough time to perform his maneuver before merging into the traffic. (a) What is the probability that the truck driver is able to join the traffic immediately on his arrival at the intersection with the service road? (b) What is the mathematical expectation of the gap (in seconds) between the truck and the nearest vehicle when the truck driver merges into the traffic? (c) Calculate the average number of vehicles that the truck driver must let go by before being able to merge into the traffic.
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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Transcribed Image Text:A truck driver is weiting to join the traffic on the service road of a highway.
The truck driver blocks the service road for four seconds when be joins the
traffic. Suppose that vehicles arrive according to a Poisson process and that
six seconds elapse, on average, between two consecutive vehicles. Answer the
following questions by assuming that the truck driver makes sure that he has
enough time to perform his nmaneuver before merging into the traffic.
(a) What is the probability that the truck driver is able to join the traffic
immediately on his arrival at the intersection with the service road?
(b) What is the mathematical expectation of the gap (in seconds) between the
truck and the nearest vehicle when the truck driver merges into the traffic?
(c) Calculate the average number of vehicles that the truck driver must let go
by before being able to merge into the traffic.
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