Analogous to poisson distribution, but for continuous random variable. Consider a distribution which lasts a duration of time until success; what’s the probability that success is found in some range of times: “What’s the probability that there are an earthquake in k years if there’s on average 2 earthquakes in 1 year?” constituents λ—“rate”: event rate (mean occurrence per time) requirements \begin{equation} f(x) = \begin{cases} \lambda e^{-\lambda x}, x\geq 0\ 0, x< 0 \end{cases} \end{equation} additional information expectation: \frac{1}{\lambda} variance: \frac{1}{\lambda^{2}} exponential distribution is memoryless An exponential distribution doesn’t care about what happened before. “On average, we have a request every 5 minutes. There have been 2 minutes with no requests. What’s the probability that the next request is in 10 minutes?” is the same statement as “On average, we have a request every 5 minutes. There have been 2 minutes with no requests. What’s the probability that the next request is in 10 minutes?” That is: