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}].
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 12CR
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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}].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F419ef6db-92c8-437a-a89f-3cae2cc1b951%2Fb8ca43f2-4447-421f-a8fe-7cdf1dfdef52%2Fcltu24i_processed.jpeg&w=3840&q=75)
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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