How do I generate a Poisson Process?

Question

Original Question:

I want to generate a Poisson process. If the number of arrivals by time t is N(t) and I have a Poisson distribution with parameter

Answer 1

In order to pick a sample from a distribution, you need to compute the inverse cumulative distribution function (CDF). You first pick a random number uniformly on the real interval [0, 1], and then take the inverse CDF of that value.