关于中心极限定理的几点注记

A few notes on central limit theorems

中心极限定理是概率论的一类重要的基础性定理,应用非常广泛,但基于理论性较强,不易掌握。就林德伯格-列维中心极限定理、棣莫弗-拉普拉斯中心极限定理及李雅普诺夫中心极限定理,分析定理的条件和结论,指出三个中心极限定理的关系,提出六点注记,得到几个实用的定理。

Central limit theorem is an important basic theorem of probability theory and it has been put into use widely. How-ever, because of its complicated theory, it is difficult for people to grasp the theorem. Lindeberg-Levy central limit theorem, Demoivre-Laplace central limit theorem and Liapounoff central limit theorem were studied in the paper. By analyzing the conditions and the conclusions of the theorems, we discussed the relations of the three central limit theorems and pointed out a few notes. At last some practical theorems were gained.