Abstract

In this paper, we consider generalizations of the optimal choice problem. There is a sequence of n identically distributed random variables on the interval [0, 1]. Sequentially obtaining the observed values of these quantities, it is necessary at some point to stop at one of them, taking it as the starting point for counting the upper or lower record values. In the optimal choice problem and its generalizations, it is required to make the correct choice of the starting point of the records in order to maximize the mathematical expectation of the sum of values or the number of upper, lower, or both record values obtained as a result of such a procedure. A review of the results on the uniform distribution of random variables and new results on the exponential distribution of random variables are presented.

中文翻译：

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关于最优选择问题的概括

摘要

在本文中，我们考虑了最优选择问题的一般化。在区间[0，1]上有n个相同分布的随机变量的序列。顺序获取这些量的观测值，有必要在某一点停止，将其作为计算上下记录值的起点。在最佳选择问题及其概括中，需要正确选择记录的起点，以最大程度地利用数值总和或上，下或两个记录值的数目的数学期望，得出这样的程序的结果。提出了关于随机变量的均匀分布的结果的综述，以及关于随机变量的指数分布的新结果。