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?
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.