Poissoneloszlású

Poissoneloszlású refers to a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is often used to model the number of events that occur in a fixed interval of time or space, such as the number of customers arriving at a store per hour, the number of phone calls received by a call center per minute, or the number of defects in a manufactured product.

The Poisson distribution is characterized by a single parameter, lambda (λ), which represents the average rate of events in the given interval. The probability mass function of the Poisson distribution is given by P(X=k) = (λ^k * e^-λ) / k!, where X is the random variable representing the number of events, k is the number of occurrences, λ is the average rate of occurrence, e is Euler's number (approximately 2.71828), and k! is the factorial of k.

Key properties of the Poisson distribution include its mean and variance, both of which are equal to λ. It is a limiting case of the binomial distribution when the number of trials is large and the probability of success is small. The Poisson distribution is widely applied in various fields, including queuing theory, reliability engineering, and physics, for modeling rare events or events occurring at a constant average rate.