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Let Xᵢ 0 be independent, i = 1, , n, and X^ₙ = (X₁, , Xₙ). Let t (c) (s (c) ) be the threshold stopping rule for X₁, , Xₙ, defined by t (c) = smallest i for which Xᵢ c (s (c) = smallest i for which Xᵢ > c), = n otherwise. Let m be a median of the distribution of X^ₙ. It is shown that for every n and X either EX^ₙ 2EXₓ (₌) or EX^ₙ 2EXₒ (₌). This improves previously known results, 1, 4. Some results for i. i. d. Xᵢ are also included.
Ester Samuel‐Cahn (Thu,) studied this question.