A Filing Problem

n samples are drawn from a known distribution, ordered and placed in groups inside file drawers with a previously decided number of samples going in each drawer; the initial (ordered) sample in a drawer defines the “beginning” of a drawer, and the initial (ordered) sample of the next drawer defines the “end” of the drawer under consideration. If N new samples are drawn from the same distribution, what is the probability that x of them fall “inside” a given filing drawer? Is it shown that this probability depends only on the number of original samples “inside” a drawer, and is independent of the original sampling distributions and of the original sample which defines the beginning of the drawer. Hence, if the design objective is to equalize the overflow probability of each drawer, the best a priori policy is to divide the original ordered samples equally among the file drawers.