Poisson - 10 things to know with detail
- 1. Poisson distribution is a probability distribution that describes the number of events occurring in a fixed interval of time or space.
- 2. It is named after French mathematician Siméon Denis Poisson, who first introduced it in the early 19th century.
- 3. The Poisson distribution is characterized by a single parameter λ (lambda), which represents the average rate of occurrence of the events.
- 4. The probability mass function of the Poisson distribution is given by P(X = k) = (e^(-λ) * λ^k) / k!, where X is the random variable representing the number of events, k is the number of events, e is the base of the natural logarithm, and ! denotes factorial.
- 5. The Poisson distribution is often used to model rare events, such as the number of customer arrivals at a service center, the number of phone calls received in a call center, or the number of defects in a product.
- 6. The Poisson distribution assumes that the events occur independently of each other and at a constant average rate throughout the interval of interest.
- 7. The mean and variance of a Poisson distribution are both equal to λ.
- 8. The Poisson distribution is a limiting case of the binomial distribution when the number of trials is large and the probability of success is small.
- 9. The Poisson distribution is commonly used in various fields such as finance, biology, telecommunications, and reliability analysis.
- 10. The Poisson distribution has several applications in real-world scenarios, such as modeling traffic flow, predicting the number of accidents in a given period, and estimating the number of emails received in a mailbox.