Poisson distribution was derived in 1837 by a French mathematician Simeon D. Poisson (1781-1840). When the likelihood of an event occurring is very low and there are a significant number of possible occurrences, the Poisson distribution can be used to explain the behavior of discrete random variables. As a result, the Poisson distribution has found use in many different domains, including Queuing Theory (issues involving waiting times), insurance, physics, biology, business, and economics.

The majority of spatial distributions, which deal with events that are intended to occur in intervals of equal length along a straight line, and temporal distributions, which deal with events that are supposed to occur in equal intervals of time, adhere to the Poisson Probability Law.

Poisson distribution is a discrete probability distribution since the variable X can take

only integral values 0, 1, 2, … ∞. The mean and variance of the Poisson distribution are both equal to the parameter value λ (lambda).

**Poisson Distribution Calculator:**

The Poisson Distribution Calculator below calculates the probability that a Poisson random variable takes a value equal to the given value of x. It also calculates the probabilities of taking value less than x, less than equal to x, more than x, and more than equal to x.

P(X = 3): 0.14037

P(X < 3): 0.12465

P(X ≤ 3): 0.26503

P(X > 3): 0.73497

P(X ≥ 3): 0.87535