完全区间树顶点数目的大数律

The Law of Large Numbers of the Size of Complete Interval Trees

本文讨论完全区间树顶点数目Sx的大数律,所采用的方法不同于单边区间树．文章包括三部分内容:首先探讨完全区间树所得以定义的概率空间,弄清楚它的结构,为强大数律的研究奠定理论基础．接着,针对完全区间树上的Sx的矩母函数不易求得的情况,另辟蹊径,求得Sx的期望和方差．最后,给出Sx的强弱大数律．

In this paper, we mainly discuss the law of large numbers of Sx, the number of vertexes on an complete interval tree. The method we use is much different from that was used in the case of one-side interval trees. First, we discuss the probability space, on which the interval trees are defined; and make clean its construction; which is the foundation for researching the strong law of large numbers. Second, considering that the moment generation functions of r.v. Sx are difficult to obtain, we use a new method to calculate its expectations and variations. Finally, we prove the weak and strong law of large numbers of r.v Sx.