I have a program running in real-time, with variable framerate, e.g. can be 15 fps, can be 60fps. I want an event to happen, on average, once every 5 seconds. Each frame, I want to call a function which takes the time since last frame as input, and returns True on average once every 5 seconds of elapsed-time given it's called. I figure something to do with Poisson distribution.. how would I do this?
It really depends what distribution you want to use, all you specified was the mean. I would, like you said, expect that a Poisson distribution would suit your needs nicely but you also put "uniform random variable" in the title which is a different distribution, anyway let's just go with the former.
So if a Poisson distribution is what you want, you can generate samples pretty easily using the cumulative density function. Just follow the pseudocode here: Generating Poisson RVs, with 5 seconds being your value for lambda. Let's call this function Poisson_RN().
The algorithm at this point is pretty simple.
global float next_time = current_time()
boolean function foo()
if (next_time < current_time())
next_time = current_time() + Poisson_RN();
return true;
return false;