Mathematics, 21.07.2020 20:01 cxttiemsp021

At a border inspection station, vehicles arrive at the rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume there are only one lane and one inspector, who can inspect vehicles ar the rate of per hour in an exponentially distributed fashion. A. What is the average length or the waiting line?
B. What is the average total time it takes for a vehicle to get through the system?
C. What is the utilization of the inspector?
D. What is the probability that when you arrive there will be three or more vehicles ahead of you?

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