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They can balance but still be random -- that's the essence of drawing without replacement, or the hypergeometric distribution. What you probably mean is that t
by kqr 3y ago
They can balance but still be random -- that's the essence of drawing without replacement, or the hypergeometric distribution.
What you probably mean is that they are no longer independent.
- 082349872349872 3y agoYou're right. (I'd count enforcement of "without replacement" as a force; at least for classical walks it'd require some kind of Maxwell daemon?) I guess what I want to get at: a Galton board is easily understood by elementary school students (and probably constructible by those in the upper grades), and it doesn't take much time playing with one to notice that all the balls don't wind up with their paths balanced out, in the middle column. (even the normal distribution is misleading, because centrality is a 1D phenomenon; given enough dimensions observing the exact average becomes exceedingly unlikely)
- kqr 3y agoIf you take the same Galton board and focud on the paths taken by all balls that ended up in a particular bin you get the hypergeometric distribution for the steps they have taken. So the draws without replacement lurk in the Galton board too. It does, in other words, not require a demon, only a restricted viewing angle.
- 082349872349872 3y agoTIL! > Page unintentionally left blank. —CS Skämtar du med mig?