10.18 Using a software package, simulate a one-dimensional Poisson process with rate 2 events/min. Using your simulation, estimate the following probabilities:

P{N[2,4] = 4}, P{S3 ∈ [3, 5]}, where N[2,4] denotes the number of events in the time interval [2, 4] minutes, and S3 is the time of the third event.

Calculate what these theoretical probabilities should be and see what the difference between your simulated probabilities and the theoretical ones was for 1000, 10, 000 and 100, 000 repetitions, respectively.