Poissonlambdas

Poissonlambdas, also known as Poisson processes with rate parameter lambda, are a type of stochastic process used in probability theory and statistics. They are characterized by the number of events occurring within a fixed interval of time or space, with the key property that these events happen independently and at a constant average rate. The parameter lambda, often referred to as the rate or intensity, represents the average number of events per unit of time or space. For example, in a Poisson process with lambda = 2, on average, two events occur per unit time. The probability of a certain number of events occurring in a given interval follows a Poisson distribution, which is given by the formula P(k events in interval) = (lambda*t)^k * e^(-lambda*t) / k!, where t is the length of the interval and k is the number of events. Poissonlambdas are widely used in various fields, including queuing theory, reliability engineering, and telecommunications, to model and analyze systems where events occur randomly and independently.