If arrivals follow a Poisson distribution, waiting times follow the exponential distribution.

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Quizplus · Accepted Answer

This is a standard result in queueing theory. The Poisson distribution is used to model the arrival process in many real-world systems, and the exponential distribution describes the time between arrivals, which is commonly referred to as the interarrival time. The intuition behind this is that Poisson arrivals are memoryless, meaning that the probability of waiting a certain amount of time for the next arrival does not depend on how long it has been since the last arrival. This property is captured by the exponential distribution, which has a constant failure rate and does not depend on time.

If Arrivals Follow a Poisson Distribution, Waiting Times Follow the Exponential