Even for bus systems that do not run on time, whether or not one bus is late affects the arrival time of the next bus. However, this is not a true Poisson process because the arrivals are not independent of one another. (One instance frequently given for a Poisson Process is bus arrivals (or trains or now Ubers). In the stock case, we might know the average movements per day (events per time), but we could also have a Poisson process for the number of trees in an acre (events per area). Poisson processes are generally associated with time, but they do not have to be. With our website, the entire interval may be 600 days, but each sub-interval - one day - our website either goes down or it doesn’t.Ĭommon examples of Poisson processes are customers calling a help center, visitors to a website, radioactive decay in atoms, photons arriving at a space telescope, and movements in a stock price. The last point - events are not simultaneous - means we can think of each sub-interval of a Poisson process as a Bernoulli Trial, that is, either a success or a failure. Two events cannot occur at the same time. ![]() ![]() The average rate (events per time period) is constant. ![]() The occurrence of one event does not affect the probability another event will occur. We might have back-to-back failures, but we could also go years between failures due to the randomness of the process.Ī Poisson Process meets the following criteria (in reality many phenomena modeled as Poisson processes don’t meet these exactly): The important point is we know the average time between events but they are randomly spaced ( stochastic). Example Poisson Process with average time between events of 60 days.
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