Key points are not available for this paper at this time.
Implicitly defined (and easily approximated) universal constants 1. 1 < aₙ < 1. 6, n = 2, 3, , are found so that if X₁, X₂, are i. i. d. non-negative random variables and if Tₙ is the set of stop rules for X₁, , Xₙ, then E (\X₁, , Xₙ\) aₙ \EXₜ: t Tₙ\, and the bound aₙ is best possible. Similar universal constants 0 < bₙ < 14 are found so that if the \Xᵢ\ are i. i. d. random variables taking values only in a, b, then E (\X₁, , Xₙ\) \EXₜ: t Tₙ\ + bₙ (b - a), where again the bound bₙ is best possible. In both situations, extremal distributions for which equality is attained (or nearly attained) are given in implicit form.
Hill et al. (Sat,) studied this question.