Question: a poisson distribution

I'm solving a differential equation in a region of appearing and disappearing potential energy, hence there is a piecewise function in the PDE w.r.t. time. The potential disappears randomly, and I need to generate a set of random times about a mean that I can put into the piecewise function to achieve this. What is the best way of generating random numbers modelled by a Poisson distribution so they can be fed into a function? Any help appreciated, Ryan
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