Poisson distribution is a discrete probability distribution which is described by a single parameter λ, the mean of the distribution. Poisson distribution is the limiting form of Binomial distribution as n -> $\infty$. It serves as an approximation to Binomial distribution when the number of trials n is very large.

Poisson distribution is used to find probabilities when

  1. n is very large and p is very small when compared to n.
  2. the discrete variable measures the density, that is when the events are counted within an interval of time, length, area , volume etc.

Poisson distribution is also used as an approximation to binomial distribution when np < 5 and for situations when only the mean of the distribution is known.

A Poisson variable is used to represent

  1. The number of natural calamities like earth quakes happening during the course of an year.
  2. The number of deaths of the insurance policy holders before the maturity period.
  3. Number of incoming calls during a period of time.

Poisson distribution is the discrete probability distribution that gives the probability of occurrence of events within a given interval of time or any n dimensional space. It is defined completely by a single parameter λ the mean number of occurrences.
P( X : λ) = $\frac{e^{-\lambda }\lambda ^{X}}{X!}$ where λ is the mean of the distribution.