Abstract
Consider a probability measure $\mu$ on $[0, 1]$ and independent identically distributed random variables $X_1,\cdots, X_n$ distributed according to $\mu$. Denote by $Q_n = Q_n (X_1,\cdots, X_n)$ the minimum number of unit-size bins needed to pack items of size $X_1,\cdots, X_n$. Previous estimates of $Q_n$ are considerably improved and simplified. Similar estimates are obtained for the maximum number of unit-size bins that can be covered by $X_1,\cdots, X_n$.
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