Poisson Distribution Calculator
Calculate probabilities and percentiles for the Poisson distribution.
Frequently Asked Questions (FAQs):
- What is the Poisson distribution, and why is it important?
- The Poisson distribution is a probability distribution that describes the number of events that occur within a fixed interval of time or space, given a known average rate. It's essential in various fields, such as modeling rare events like phone call arrivals, accidents, or natural phenomena.
- What is the formula for calculating the Poisson distribution?
- The formula for the Poisson distribution probability of observing exactly k events in a fixed interval, when the average rate is λ, is:
- Where e is Euler's number (approximately 2.71828), λ is the average rate, k is the number of events, and k! is the factorial of k.
- How do I interpret the Poisson distribution values?
- The Poisson distribution values provide the probabilities of observing different numbers of events in a fixed interval. Larger values of λ result in a higher likelihood of observing more events, while smaller values lead to a lower likelihood of observing many events.