Some distributions that allow perfect packing

A probability distribution <italic>μ</italic> on [0, 1] allows perfect packing if <italic>n</italic> items of size <italic>X</italic><subscrpt>1</subscrpt>, … , <italic>X</italic><subscrpt><italic>n</italic></subscrpt>, independent and identically distributed according to <italic>μ</italic> can be packed in unit size bins in such a way that the expected wasted space is <italic>o</italic>(<italic>n</italic>). A large class of distributions that allow perfect packing is exhibited. As a corollary, the intervals [<italic>a, b</italic>] for which the uniform distribution on [<italic>a, b</italic>] allows perfect packing are determined.