随机变量序列X_n服从大数定律的充要条件

Sufficient and Necessary Conditions for the Sequences X_n of Random Variables Obeying Major Princi

摘要: 首先给出大数定律的基本形式,在几个引理的基础上,提出并证明了Xn服从大数定律的充要条件是E1 Y+2nY2n→0(n→∞),其中Yn=n-1k∑=n1(Xk-μk),μk=EXk(k=1,2,…).

Abstract: The basic forms of major principles are presented firstly.Then that Xn obeys the major principles if and only if EY2n 1+Y2n→0(n→∞),where Yn=n-1∑n k=1(Xk-μk),μk=EXk(k=1,2,…),is proved on the base of some lemmas.