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49. Cars arrive at the beginning of a long road in a Poisson stream of rate from time t = 0 onwards. A car has a fixed velocity V> 0 which is a random variable. The velocities of cars are independent and identically distributed, and independent of the arrival process. Cars can overtake each other freely. Show that the number of cars on the first x miles of the road at time t has the Poisson distribution with parameter λE[V-1 min {x, Vt}].

49. Cars arrive at the beginning of a long road in a Poisson stream of rate from time t = 0 onwards. A car has a fixed velocity V> 0 which is a random variable. The velocities of cars are independent and identically distributed, and independent of the arrival process. Cars can overtake each other freely. Show that the number of cars on the first x miles of the road at time t has the Poisson distribution with parameter λE[V-1 min {x, Vt}].

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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49. Cars arrive at the beginning of a long road in a Poisson stream of rate from time t = 0 onwards. A car has a fixed velocity V> 0 which is a random variable. The velocities of cars are independent and identically distributed, and independent of the arrival process. Cars can overtake each other freely. Show that the number of cars on the first x miles of the road at time t has the Poisson distribution with parameter λE[V-¹ min {x, Vt}].
Transcribed Image Text:49. Cars arrive at the beginning of a long road in a Poisson stream of rate from time t = 0 onwards. A car has a fixed velocity V> 0 which is a random variable. The velocities of cars are independent and identically distributed, and independent of the arrival process. Cars can overtake each other freely. Show that the number of cars on the first x miles of the road at time t has the Poisson distribution with parameter λE[V-¹ min {x, Vt}].
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