Optimal Bin Packing with Items of Random Sizes

Consider a probability μ on [0, 1] and i.i.d. random variables X₁, X₂, …, X_n distributed like μ. Let Q_n denote the optimal (minimum) number of unit size bins needed to pack items of size X₁, X₂, …, X_n. We characterize the class of μ which have the property that lim_n→∞Q_n/n = E(X₁) a.s., or equivalently that the expected level of occupancy of bins converges to one.