# Poisson Distribution

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**

- n is very large and p is very small when compared to n.
- 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

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