Poisson Distribution Calculator

Easily calculate Poisson probabilities and visualize the distribution.

Understanding Poisson Distribution

The Poisson distribution is a discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

It is often used to model the number of rare events such as accidents, defects, or arrivals in queues.
Key parameters are: λ (lambda), the average rate of events.
Formula: $$P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}$$, where k is the number of events.

Average rate of occurrence (λ)

The average number of events per interval (must be non-negative).

Number of events (k)

The number of events for which to calculate the probability (must be non-negative integer).

Probability of events:

$$P(X=) = $$

Poisson Distribution Visualization

Poisson Distribution: Quick Guide

What is Poisson Distribution?

Poisson distribution is used to model the probability of a certain number of events happening within a fixed interval of time or space. It's applicable when events occur randomly and independently at a constant average rate. Examples include the number of phone calls received by a call center per hour, or the number of emails received per day.

Key Concepts

λ (Lambda): Represents the average rate of events. It's a crucial parameter that defines the distribution.
k: The number of events you want to find the probability for.
Independence: Events must be independent of each other.
Constant Rate: The average rate of events (λ) must be constant over the interval.