4 ms·
random variable as a shortening of "measurable function from a probability space" doesn't seem too bad to me
by ginnungagap 8y ago
random variable as a shortening of "measurable function from a probability space" doesn't seem too bad to me
- sorokod 8y agoDon't see how this works as the extended version doesn't mention random or variable.
- ginnungagap 8y agoMy point is that is isn't just a function, but a measurable one (with weak restriction on the measure space it has as domain) so we can't call it just "function" as you were suggesting. The actual name might be debatable, but a shortened name rather than the full definition definitely makes sense here. Random variable seems like a good choice of name to me, thinking about the intuition we're formalizing with it.
- tangentspace 8y agoBut you propose to simply relabel as function, which doesn't work in general because random variable corresponds to a specific type of function. You could compromise by calling it a probability function, but then you start to collide with other uses of that word. I agree random variable is awkward, though. I always avoided stats courses because it's full of so much jargon that collides with nomenclature used by mathematicians.
- sorokod 8y agoYes, it's not just a function - there are strings attached but we deserve a better name - probability function is x100 better. "random variable" is exceptionally bad in that it leads the mind in irrelevant directions.
- tangentspace 8y agoTo follow one of the more common patterns for identifying a class of functions, it could have been named after one of the early pioneers in the field. But yeah, it would be hard to do worse than random variable, which is illogical and misleading. I found this doc on the origins of the name (author also agrees it's terrible): http://www.glennshafer.com/assets/downloads/talks164_The-invention-of-random-variables.pdf http://www.glennshafer.com/assets/downloads/talks164_The-inv... Sounds like it got mangled as work was being translated back and forth between Russian, English, French, and German.
- sorokod 8y agoAnother approach is to use language not commonly spoken ( quickly - what does topology means) and consequently less burdened with cultural baggage.