Optimal Bin Packing of Items of Sizes Uniformly Distributed over [0, 1]

Consider n independent random variables uniformly distributed over [0, 1] and consider the minimum number B^k of unit size bins needed to pack these items under the restriction that no bin can accept more than k items. We prove that EB² − EB³ is of order √n. But in sharp contrast, we show that EB³ − EBⁿ is of a smaller order.