The Poisson Distribution

The Poisson distribution is most commonly used to model the number of random occurrences of some phenomenon in a specified unit of space or time. For example,

• The number of phone calls received by a telephone operator in a 10-minute period.
• The number of flaws in a bolt of fabric.
• The number of typos per page made by a secretary.

For a Poisson random variable, the probability that X is some value x is given by the formula

where is the average number of occurrences in the specified interval. For the Poisson distribution,

EXAMPLE:\ The number of false fire alarms in a suburb of Houston averages 2.1 per day. Assuming that a Poisson distribution is appropriate, the probability that 4 false alarms will occur on a given day is given by