# Manuals/calci/POISSON

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

1. POISSON(10,3,TRUE) = 0.9997076630493528
2. POISSON(10,3,FALSE) = 0.0008101511794681433
3. POISSON(21.7,7.54,TRUE) = 0.9999955033358848
4. POISSON(21.7,7.54,FALSE) = 0.00000948031184308478

## Related Videos

Poisson Distribution