POISSON(x, mean, cumulative)

The POISSON function calculates the Poisson distribution. This is useful for predicting the probability of a number of events over a specific measure, for example time, length or area.

The arguments of the function represent the following:

x

the number of events, for which we seek the probability

mean

the known average rate of events

cumulative

a logical value, which determines the form of the function:

TRUE calculates the cumulative Poisson probability, which gives the probability that the number of events will be between 0 and x inclusive.

FALSE calculates the Poisson probability mass function, which gives the probability that the number of events will be exactly x.

For example, if 7 cars per minute is the average traffic rate on a particular road, and their arrival is entirely random, we can calculate the probability of there being exactly 4 cars in a minute by using the formula:

POISSON(4, 7, FALSE)

which returns a probability of 0.091226.

The probability that there will be between 0 and 4 cars per minute inclusive is given by:

POISSON(4, 7, TRUE)

that is 0.172992.

See also:

Other statistical functions