关于游程的一个发生函数的研究

Research on a Generation Function of Runs

游程及其相关理论广泛地应用于随机检验、质量控制、DNA数据分析等许多领域,提出使用组合数学的方法推导出贝努利试验中最长游程的概率发生函数的计算公式,利用所得到的结果可以不用k阶几何分布的概率函数而很容易地得出它的概率发生函数.

Run and the correlated theory have been applied to many fields widely, for example, random test, quality control, data analysis of DNA and so on. In this paper the method of combinational mathematics is used to deduce the probability generation function of the longest run in the Bernoulli trials, and get the probability generation function without using its probability function of kth order geometric distribution.