Probability Distribution Function (PDF) of Poisson Distribution
The Probability Density Function (PDF) of a Poisson distribution helps in determining the chance of a certain number of events happening within a set time or space. It is handy when events are infrequent and happen independently. For instance, imagine a bakery. Customers arrive randomly at an average rate of 4 customers per hour. We can apply the Poisson distribution to calculate the probability of a specific number of customers arriving in one hour. The PDF of Poisson Distribution can be written as:
P(X = x) = , x = 1, 2, 3,……..; >0
Where,
- P(x) represents the probability of a specific number of events occurring.
- e is the mathematical constant approximately equal to 2.7183.
- λ is the average rate of event occurrences in the given time or space.