常用概率分布间的关系

The Relationships among the Commonly Used Probability Distributions

随机变量的概率分布是概率论和数理统计教学中的最基本的概念,在初级教程中一般都是孤立地阐述各种概率分布.为使学生建立起常用概率分布之间的联系,本文对常用8种离散型概率分布和15种连续型概率分布的关系加以讨论,主要概括归纳成4种关系,分别是由极限、变换、独立同分布的和以及特殊情形生成的关系.并在讨论它们关系的基础上,建立起分布间的关系图来进一步阐述,以加深理解.并对该关系图的建立过程加以说明.

The proba ry and mathematical bility stati distribution of random variable is the most basic concept of probability theostics in teaching. In general, the different probability distributions are discussed separately in primary course. To set up the connection of commonly used probability distributions, this paper discusses the relationships among 8 commonly used discrete probability distributions and 15 commonly used continuous probability distributions. There are 4 primary relationships. They are limit, transform, sum of independent same distribution and relationship created by special conditions. And more statement of the relationship chart among distributions are made on the basic of discussion of their relationships. It explains the establishment of the relationship chart.