惠更斯的5个概率问题

Huygens' Five Problems on Probability

中文关键词:  概率论  惠更斯  递推法  数学期望  骰子.

英文关键词:probability  huygens  recursion  expectation  dice.

中文摘要:

      惠更斯在第一部概率论著作《论赌博中的计算》中提出5个概率问题,但均无求解过程. 这5个问题既可看作实际问题,又可看作该书中命题的延伸. 这些问题以机会问题为研究对象,把赌博问题的分析提升到一定的理论高度. 这就为概率论的进一步发展奠定了坚实基础. 本文尝试以惠更斯的方法来解决这些问题,再对比今日所用之法,从中得到若干结论.

英文摘要:

      Huygens has put forward five problems in his book, but without solution. These problems can be regarded as both resolving practice questions and prolongation of the propositions in his book. He advanced the probability questions to generalization, which laid the foundation for further development. This paper attempts to testify these problems by the Huygens' method and compare them modern methods.