In 1837 French mathematician Simeon Dennis Poisson derived the distribution as a limiting case of Binomial distribution. It is called after his name as Poisson distribution.

A random variable X is said to follow a Poisson distribution if it assumes only non-negative integral values

In a Binomial distribution with parameter n and p if the exact value of n is not definitely known and if p is very small then it is not possible to the find the binomial probabilities .

Even if n is known and it is very large, calculations are tedious. In such situations a distribution called Poisson distribution is very much useful.

The number of trails 'n' is indefinitely large i.e., n→ ∞

The probability of a success 'p' for each trial is very small i.e., p → 0

np= λ is finite

Events are Independent

Poisson distribution is a discrete distribution
i.e., X can take values 0, 1, 2,…

p is small, q is large and n is indefinitely large
i.e., p →0 q →1 and n→3 and np is finite

Values of constants :
(a) Mean = λ = variance
(b) Standard deviation = √λ
(c) Skewness = 1/ √λ
(iv) Kurtosis =1/ λ

It may have one or two modes.

If X and Y are two independent Poisson variates, X+Y is also a Poisson variate.

If X and Y are two independent Poisson variates, X-Y need not be a Poisson variate.

Poisson distribution is positively skewed.

It is leptokurtic.

The number of mistakes committed in a typed page.

The number of death claims received per day by an insurance company.

The event of a student getting first mark in all subjects and at all the examinations.

The number of blinds born in a particular year.

The number of traffic accidents per day at a busy junction