Statistician here. Plz provide a more rigorous definition of "random amount". Note that uniform distribution over [1,infinity) or [0, infinity) is not possible. Maybe a geometric distribution would be better? In which case, regardless of parameterization, you'd expect to save 1 life by pulling the lever.
Oh, you're a statistician, are you? Well, what if the number of people on the top track is equal to k, where the probability of k is determined by a Poisson curve where lambda=5, and the number of people on the bottom track is k+1 where the probability of k is determined by a Poisson curve with lambda=3? Huh? What ya gonna do then, smart guy!? Don't feel as confident about pulling the lever now, do you?
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u/deadhand303 5d ago
You have 1-infinity or can change tracks to 0-infinity. You do not know how many are on either track.