# Documentation/How Tos/Calc: POISSON function

CALC FUNCTIONS
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## POISSON

Calculates values for a Poisson distribution.

### Syntax:

POISSON(x; λ; mode)

The Poisson distribution is a discrete probability distribution giving the probability that x events occur in a certain time, where events occur independently, and where on average λ events are expected. x should be >=0 and λ should be >0. x should be integer.
If mode is 0, POISSON calculates the probability density function of the Poisson distribution: If mode is 1, POISSON calculates the cumulative distribution function of the Poisson distribution: ### Example:

POISSON(8; 9; 0)

returns approximately 0.1317, the probability that exactly 8 events occur in a time period where you expect 9 events.

POISSON(8; 9; 1)

returns approximately 0.4556, the probability that up to and including 8 events occur in a time period where you expect 9 events.