2.2.1.3 Poisson Distribution

Poisson Distribution is a distribution that describes the probability of a given number of events occurring within a fixed time interval or region of opportunity (like Distance, Volume, Area, etc.). The distribution has some key characteristics:

• The number of occurrences in each interval range from zero to infinity
• Each event is independent of the other events i.e., the occurrence of one event should not affect the occurrence of a subsequent event
• The average rate (events per interval) is constant.

Say, the number of visitors to a website or the number of calls received by a call center per hour.

Poisson distribution can be calculated through the following formula:

Where:

•  is the actual number of successes that occur within a specific interval
•  = (mean), is the number of successes that occur within a specific interval
•  is the Euler's constant, equal to approximately 2.71828

Example 2.3. Imagine a call centre receives 8 calls in an hour, find the probability of the following scenarios:

1. Exactly 10 calls in an hour
2. At least 10 calls in an hour

Here, the values of λ and  are the same for all the scenarios:

•  = 8
•  = 2.71828

Scenario 1: Exactly 10 calls in an hour

Here,  = 10

Substituting the values of , , and  in the Poisson distribution formula yields: