Poisson distribution

In probability and statistics, Poisson distribution is a probability distribution. It is named after Siméon Denis Poisson. It measures the probability that a certain number of events occur within a certain period of time. The events need to be unrelated to each other. They also need to occur with a known average rate, represented by the symbol  (lambda). 

More specifically, if a random variable  follows Poisson distribution with rate , then the probability of the different values of  can be described as follows: 

    for  

Examples of Poisson distribution include:
 The numbers of cars that pass on a certain road in a certain time
 The number of telephone calls a call center receives per minute
 The number of light bulbs that burn out (fail) in a certain amount of time
 The number of mutations in a given stretch of DNA after a certain amount of radiation
 The number of errors that occur in a system
 The number of Property & Casualty insurance claims experienced in a given period of time

 Related pages 

 Binomial distribution
 Exponential distribution

 References 

Category:Probability distributions