Waiting Times

Geometric and exponential waits

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Geometric: $P(X = k) = (1-p)^{k-1}p$, with mean $1/p$ tries.
• Independent random events are memoryless: the past doesn’t make them “due”.
• Exponential waits: the median ($\ln 2$ × mean) is shorter than the mean.

Steps

1. The geometric distribution
2. Third time lucky
3. Memoryless
4. Waiting in continuous time
5. Median versus mean
6. Half-lives