The exponential distribution models how long—or how far—it is until the next event in a Poisson process. Poisson counts events in a fixed interval; exponential models the time between consecutive events. It is continuous, so probabilities describe ranges of waiting times rather than individual values. section 3.10 section 3.12
From video views to waiting time
If a video averages 10 views per minute, the average wait is 0.1 minutes, or 6 seconds. Using scipy.stats.expon.cdf(.4, scale=1/10) gives about 0.982, meaning a 98% chance that the next view arrives within 24 seconds. Subtracting two CDF values gives the probability of landing in a middle range. section 3.10
Random draws from the distribution turn an average rate into a timeline. In a coffee-shop simulation, accumulate each exponentially generated wait until three hours have passed; the result estimates both the number and timing of espresso shots. section 3.11
