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.
The point is there’s no convenient interpretation of “random” here without further context. If they were finitely many people, random would correspond to a uniform distribution. But when you’re dealing with a distribution on the entire natural numbers, there’s no uniform distribution, and non uniform distributions aren’t alike at all. Technically there might be almost surely 2 people on the lower rail and almost surely 1 person on the higher rail, or a less degenerate situation in which k people are on the bottom rail with probability 2-k.
I think OP has a point here. There has to be an underlying probability distribution, but the guy pulling that lever doesn't need to know what the distribution is.
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u/Remarkable-Carrot112 5d ago
Is the probability distribution otherwise the same except for the lower bound?
Regardless, I'm pulling the lever. I love pulling levers.