Poisson Distribution
Overview
- The Poisson distribution models the number of events occurring in a fixed interval of time or space, given that these events occur with a constant rate and are independent of the time since the last event.
- It is often used to model rare events or phenomena where the probability of occurrence is small over a specific interval.
Use Case
- Used in various fields such as insurance (to model the number of claims per day), telecommunications (to model the number of phone calls arriving at a call center), and biology (to model the number of mutations in a DNA sequence).
- Probability Mass Function (PMF):
- : Number of events occurring in the interval
- : Average rate of events occurring in the interval (also known as the rate parameter)
- : Euler's number, approximately equal to 2.71828
Example
- Call Center:
- Suppose a call center receives on average 10 calls per hour .
- We want to find the probability of receiving exactly 5 calls in the next hour .
- Using the Poisson PMF:
