*poisson distribution calculator* - an online tool of discrete probability & statistics data analysis to find the probability of given number of events that occurred in a fixed interval of time with respect to the known average rate of events occurred. This calculator computes the output values of poisson and cumulative poisson distribution with respect to the input values of average rate of success and the random variables.

### formula

The below mathematical formula is used to find out the probability of given number of events occurred in a certain interval of time for the instances of **x = 0, 1, 2, ...., n**

where,

**e** is the base of the natural logarithm equal to **2.71828**

**x** is the number of events occurred; the probability of which is given by the function

**x!** is the *factorial of x*

**λ** is a positive real number, is the **mean** or equal to the expected number of occurrences for the given interval. For instance, if the events occurred on an average of 3 times per minute, and one is interested in the probability of events occurring x times in a 10 minute interval, one would use a poisson distribution as the model with **λ** = 10 x 3 = 30

The poisson distribution, a discrete probability function is used to estimate the degree of spread with known average rate of occurrences. When situation arise with the experiment where the great number of possible event occurs, the poisson distribution is employed to designate the probability of a given data set or number of events at a fixed time of interval. It is asymmetric function and has the strong connection with hyper-geometric, exponential & *binomial distribution calculations*.

Poisson distribution is used in various application such as Biology, Telecommunication, Astronomy, engineering, financial sectors, radioactivity, sports, surveys, IT sectors etc to find the number of events occurred in fixed time intervals. In *probability & statistics* data analysis, when it comes to online calculation, this poisson distribution formula & calculator may be useful to find out the number of events occurred in a certain time intervals.