Poisson Distribution Calculator
Calculate Poisson probability online quickly and easily. Visualize the Poisson distribution with interactive charts. Understand event probabilities with our user-friendly tool.
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.
The average number of events per interval (must be non-negative).
The number of events for which to calculate the probability (must be non-negative integer).
Probability of events:
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.
Formula
The probability of exactly k events occurring is given by: $$P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}$$ Where:
- P(X=k) is the probability of k events occurring
- λ is the average rate of events
- e is Euler's number (approximately 2.71828)
- k! is the factorial of k