On an Interval Splitting Problem
نویسندگان
چکیده
Let X,, X,, ,be i.i.d. random variables, which are uniformly distributed on [O,l]. Further let Z,(O) = [0, l] and let Z,(n) denote the k th largest interval generated by the points 0, X,, X,, . , X,_ 1, 1 (or equivalently, the interval corresponding to the kth largest spacing at the nth stage). This note studies the question for which classes of sequences k = k(n), will the interval Z,(,,(n) be hit (as.) only finitely often, as well as infinitely often.
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