The exponential distribution

The exponential distribution occurs frequently when considering situations where there are many small positive quantities and much fewer larger quantities. Given what we have learned about the Richter scale, it won't be a surprise to learn that the magnitude of earthquakes follows an exponential distribution.

The distribution also frequently occurs in waiting times—the time until the next earthquake of any magnitude roughly follows an exponential distribution as well. The distribution is often used to model failure rates, which is essentially the waiting time until a machine breaks down. Our exponential distribution models a process similar to failure—the waiting time until a visitor gets bored and leaves our site.

The exponential distribution has a number of interesting properties. One relates to the mean and standard deviation:

(defn ex-2-4 []
  (let [dwell-times (->> (load-data "dwell-times.tsv")
                         (i...