The Riddler puzzle describes a Poisson process, which is one of the most important stochastic processes. A Poisson process models the intuitive concept of “an event is equally likely to happen at any moment.” It’s named because the number of events occurring in a time interval of length is distributed according to , for some rate parameter (for this puzzle, the rate is described as one per day, ).
How can we simulate a Poisson process? This is an important connection between distributions. The waiting time for the next event in a Poisson process has an exponential distribution, which can be simulated with
Read on to learn about the Poisson distribution and Yule processes.