On the asymptotic behavior of the number of trials necessary to complete a set with random selection

The problem of collecting m copies of a set of n objects by random selection is studied. Previous efforts on this problem have assumed that the probability of selecting a particular object of the set at any trial is 1 n. In this paper it is assumed that the probability of selecting the ith object at any trial is given by pi = ∝ (i - 1) n i n f(u)du. The mean and the variance of the number of trials necessary to complete the collection are computed along with their asymptotic behavior as n → ∞. © 1963.