Poisson Distribution Calculator
Poisson Distribution Calculator Info
The Poisson distribution is a discrete probability distribution that expresses 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.
The Poisson distribution can be applied to systems with a large number of possible events, each of which is rare. Within sporting events a Poisson Distribution is often used to model things like the number of goals scored in a match.
Formula
The probability mass function of a Poisson distribution is:
P(X = k) = (λ^k * e^-λ) / k!
Where:
- λ (lambda) is the expected number of events in the interval
- k is the number of events
- e is Euler's number (approximately 2.71828)
- k! is the factorial of k
Properties
- Mean: λ
- Variance: λ
- Standard Deviation: √λ