POISSON DISTRIBUTION Meaning and
Definition
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The Poisson distribution is a probability distribution that represents the number of events that occur within a fixed interval of time or space. It is commonly used to model the frequency of rare events such as traffic accidents, phone calls, or customer arrivals at a service center.
The distribution is named after French mathematician Siméon Denis Poisson, who first introduced it in the early 19th century. It is characterized by a single parameter, denoted by λ (lambda), which represents the average rate or the expected number of events occurring in the given interval.
The Poisson distribution satisfies several key properties. Firstly, the probability of observing a certain number of events within the interval is independent of the time or space unit being observed. Secondly, the events must occur at a constant and known average rate throughout the interval. Additionally, the events must be independent of one another, meaning that the occurrence of one event does not affect the occurrence of others.
The probability mass function (PMF) of the Poisson distribution gives the probability of observing exactly k events within the interval, and it is defined as:
P(X=k) = (e^(-λ) * λ^k) / k!
Where e is the mathematical constant approximately equal to 2.71828, and k! denotes the factorial of k.
The Poisson distribution is widely used in various fields such as insurance, queuing theory, reliability analysis, and particle physics, where the occurrence of rare events is of interest.
Common Misspellings for POISSON DISTRIBUTION
- ooisson distribution
- loisson distribution
- -oisson distribution
- 0oisson distribution
- piisson distribution
- pkisson distribution
- plisson distribution
- ppisson distribution
- p0isson distribution
- p9isson distribution
- pousson distribution
- pojsson distribution
- poksson distribution
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- poiason distribution
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- poixson distribution
Etymology of POISSON DISTRIBUTION
The term "Poisson Distribution" comes from its creator, the French mathematician Siméon Denis Poisson. Siméon Denis Poisson first introduced this probability distribution in his work "Recherches sur la probabilité des jugements en matière criminelle et en matière civile" (Research on the Probability of Judgments in Criminal and Civil Matters) published in 1837. The distribution is named in his honor to acknowledge his significant contribution to the field of probability theory.
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