摘要
通过建立随机事件的可拓模型,给出了随机事元、随机事元的概率和随机事元集的概念．在对随机事元可拓性研究的基础上给出了随机事元的传导概率的概念．利用随机事元的多特征性,讨论了当随机事元的某一个或若干个特征的量值改变时,由可拓变换的传导性,将导致随机事元其它特征的量值发生改变,从而导致随机事元概率的改变,进而为依赖于随机事件发生的概率的矛盾问题的解决提供了有效途径．最后以离散型随机变量的概率分布为例,利用随机事元集与可拓变换对随机变量的概率分布进行了初步的可拓研究,给出了传导概率分布的概念,并讨论指出了概率论中随机变量的函数的分布是传导概率分布的特例．
Firstly, the authors in this paper put forward a series of concepts such as random event element, probability of random event element and random event element sets by means of the extension modeling of random event; and the concept of the extension probability of random event element is also given on the basis of the study of the extension of random event element. Secondly, by making use of the multi - characteristics of the random event element, the authors have discussed the following case： when a certain or a few characteristics＇ quantity values of the random event element altered, because of the conductivity of the extension transformation, it will lead to the alteration of the other characteristics＇ quantity values. And therefore, this will surely lead to the change of the probability of the random event element. Sequentially, an efficient solving method for the contradiction problem that depends on the random event probability is then given. Finally, by taking the probability distribution of the discrete random variables as example and making use of the random event element sets and extension transformation, the authors have made preliminary extension research on the probability distribution of the random variables, and thereby, put forward the concept of extension probability distribution and indicate that what we call the functional distribution of random variables in the theory of probability is just the special case of the extension probability distribution.
出处
《哈尔滨工业大学学报》
EI
CAS
CSCD
北大核心
2006年第7期1108-1111,共4页
Journal of Harbin Institute of Technology
关键词
矛盾问题
随机事元
可拓性
可拓变换
传导概率
contradiction problem
random event element
extension
extension transformation
conductivity probability
