摘要
本文证明了随机变量标准差和平均差δ=E|X-EX|间的一个重要不等式:σ≥δ,等号当且仅当X服从单点分布或等概率两点分布时成立。对一些常用分布具体讨论了σ与δ间的差距,说明标准差和平均差是两个不同概念,标准差并不能度量平均差。
An important inequality between standard deviation and mean deviation δ=E|X-EX| is given :σ≥δ,the equality holds if and only if X is one-point distributed or equal probabieity two-point distributed. The difference be-tween a and δ is discussed under common used special distributions.It shows that standard deviation and mean deviation are two different conceptions,mean deviation can not be measured by standard deviation。
出处
《天津纺织工学院学报》
北大核心
1994年第2期117-120,共4页
Journal of the Tianjin Institute of Textile Science and Technology