Poisson distribution
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A Poisson distribution is a mathematical tool for describing the probability of how many times something happens in a fixed period of time or space, like the number of emails you receive in an hour or customer arrivals at a store in a day. It's useful because many real-world events that occur randomly and independently follow this pattern, making it easier to predict and plan for these kinds of situations.
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In probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. It can also be used for the number of events in other types of intervals than time, and in dimension greater than 1 (e.g., number of events in a given area or volume). The Poisson distribution is named after French mathematician Siméon Denis Poisson. It plays an important role for discrete-stable distributions.
Under a Poisson distribution with the expectation of λ events in a given interval, the probability of k events in the same interval is: