# Poisson Distribution

It is named after the French Mathematician Simeon Denis Poisson (1781 −1840) who discovered it. Poisson distribution is a discrete distribution. Poisson distribution is a limiting case of Binomial distribution under the following conditions:

• (i) nthe number of trials is indefinitely large, n → ∞.
• (ii) p the constant probability of success in each trial is very small, p → 0.
• (iii) np = λ is finite where λ is a positive real number.

When an event occurs rarely, the distribution of such an event may be assumed to follow a Poisson distribution.

### Definition

A random variable X is said to have a Poisson distribution if the probability mass function of X is The mean of the Poisson Distribution is λ, and the variance is also λ. The parameter of the Poisson distribution is λ.

### Examples of Poisson Distribution

1. The number of alpha particles emitted by a radio active source in a given time interval.
2. The number of telephone calls received at a telephone exchange in a given time interval.
3. The number of defective articles in a packet of 100, produced by a good industry.
4. The number of printing errors at each page of a book by a good publication.
5. The number of road accidents reported in a city at a particular junction at a particular time.