# Manuals/calci/POISSON

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**POISSON(X,Lambda,Cumulative)**

- is the number of events.
- is the mean
- is the logical value like TRUE or FALSE.
- POISSON(), returns the Poisson distribution.

## Description

- This function gives the value of the Poisson distribution.
- The Poisson distribution is a discrete probability distribution for the counts of events that occur randomly in a given interval of time.
- It is is used to model the number of events occurring within a given time interval.
- In , is the number of events in a given interval of time, is the Average Numeric value and is the logical value.
- If it is TRUE, this function will give the Cumulative Poisson Probability with the number of random events between and (included).
- If it is FALSE, this function will give the Poisson Probability Mass function with the number of events occurring will be exactly .
- The probability mass function is:

where is the shape parameter and . is the base of the natural logarithm (e=2.718282).

- The Cumulative Poisson Probability function is:

.

- This function will return the result as error when

1. or is non-numeric. 2. or .

## Examples

- POISSON(10,3,TRUE) = 0.9997076630493528
- POISSON(10,3,FALSE) = 0.0008101511794681433
- POISSON(21.7,7.54,TRUE) = 0.9999955033358848
- POISSON(21.7,7.54,FALSE) = 0.00000948031184308478

## Related Videos

## See Also

## References