Il giorno giovedì 5 marzo 2015 22:39:54 UTC+1, Damian Vicino ha scritto:
I was thinking the same approach. But it is necessary to study how the selection affects the distribution.
I don't think there exists such a thing as a "uniformly distributed rational" in some bounded interval; IOW, there's no way of defining a probability measure ( aka a totally additive bounded measure over a sigma algebra of subsets ) over a bounded interval of rationals uniformly with respect to the measure of the corresponding real interval ( indeed, note that the set of rationals in [0,1] has Lebesgue measure zero, that is, the probability that a unfirom real in [0,1] is rational is zero ). It's somewhat like asking for a *uniformly* distributed integer over [0,1,2...,+inf). Of course, this does not mean there isn't a probability distribution of rationals satisfying some special *uniformness* criteria that fits your needs, but not in any *standard* way ....