Rare Events

The Poisson distribution

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Poisson: $P(X = k) = \dfrac{\lambda^k e^{-\lambda}}{k!}$, for rare independent events at rate $\lambda$.
• Mean and variance are both $\lambda$.
• $P(\text{none}) = e^{-\lambda}$.

Steps

1. Many chances, each tiny
2. The Poisson shape
3. More chances, each rarer
4. A quiet hour
5. Typos
6. Random means clumpy
7. Kicked by horses