Poisson Distribution Calculator

Formula

The formula to calculate the Poisson probability is:

\[ P(k; \lambda) = \frac{\lambda^k e^{-\lambda}}{k!} \]

Where:

\( P(k; \lambda) \) is the probability of \( k \) events occurring in a fixed interval.
\( \lambda \) is the mean number of events.
\( k \) is the number of events.
\( e \) is the base of the natural logarithm (approximately equal to 2.71828).
\( k! \) is the factorial of \( k \).

Example

Let's say the mean number of events (λ) is 3, and we want to find the probability of 5 events occurring. Using the formula:

\[ P(5; 3) = \frac{3^5 e^{-3}}{5!} \approx 0.10082 \]

So, the probability of 5 events occurring is approximately 0.10082.

What is the Poisson Distribution?

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, given a known constant mean rate and independence of events.