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### 2.1.8 The Poisson Distribution

The Poisson distribution is a model for the relative frequency of rare events. It is often used to determine the probability that number of events will happen in a specific time, area or volume. The model applies to cases where each event occurs with the same probability at any part in time or location in space.

Examples

• The number of Microorganisms within a microscope field.
• The number of Neuron spikes within a 10ms period.
• Suspension of blood cells in a counting chamber: Number of cells per square of the counting chamber.

Definition 12   The Poisson distribution function with parameter (that represents the average number of events in a unit of time, area or volume) is:

Remarks:

• Often, instead of the expected number , the proportion of successful events per time area or volume unit is known. In this case can be determined by where is the number of units we consider. For example: if we know that out of people are females then if we construct a Poisson r.v. that counts the number of females within a sample of then we will use .
• When is small and is large, the Binomial distribution can be approximated with a Binomial distribution.

Next: 2.2 Limit Laws of Up: 2.1 Probabilities and Random Previous: 2.1.7 The Binomial distribution
Eran Borenstein
2007-05-04