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.


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.