基本解释：独立,互相独立
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We conclude more accrate result in this paper: set {An} is a mutually independent random sequence,if ∑∞n=1p(An)=∞,the ∑ni=1IAi/∑ni=1p(Ai)→1 a.得到比上述引理更精确的结果:设{An}是相互独立的随机事件序列,若∑∞n=1p(An)=∞,则有∑ni=1IAi/∑ni=1p(Ai)→1a。
Then the explanation that the sufficient and necessary condition of random variable ξ1+ξ2 and ξ1-ξ2 as well as ξ1cosα+ξ2sinα and-ξ1sinα+ξ2cosα are mutually independent is conducted.根据随机变量相互独立的条件,推导了二元正态分布随机变量的线性函数1η=pξ1+q2ξ与2η=m1ξ+n2ξ相互独立的充要条件是nqσ22+rσ12σ(np+mq)+mp21σ=0(其中m、n、p、q为非零实数,且np-mq≠0),并做了详细证明。
This paper,taking the two-dimensional separate random variable as an example,produced the mutually independent distinctions method for separate random variable,and made a comparison between them.以二维离散型随机变量为例,给出了离散型随机变量相互独立的几个判别方法,并对其进行了比较。
Then a necessary and sufficient condition that the random variables are independent mutually is given.讨论了多元函数与某个变量无关的充分条件及多元函数的变量能分离的充分必要条件,并给出随机变量相互独立的一个充分必要条件。
The concept of independence among participation levels is defined.本文基于经典合作博弈局中人间相互作用现象的有关度量方法,针对具有模糊联盟的合作博弈问题,给出了模糊联盟中各局中人参与水平间相互作用的度量方法,定义了水平间相互独立性概念,建立了反映局中人各参与水平间相互作用平均程度的两指标:Shapley相互作用指标及Banzhaf相互作用指标。
The independence of two dimensional random variable (X, Y) is defined by the equation F(x,y)=F X(x)·F Y(y), of which F(x,y),F X(x),F Y(y) are distribution functions to (X,Y),X and Y.二维离散型随机变量（Ｘ，Ｙ）相互独立的定义是：Ｆ（ｘ，ｙ）＝ＦＸ（ｘ）ＦＹ（ｙ）。
In this paper, two results about independence of three random variables are given.本文给出了三随机变量相互独立与条件独立的两个结论。
Culture not only blend in,but also is independent each other.文化是可融的,又是相互独立的。
Separate Random Variable for Mutually Independent Distinction Method;离散型随机变量相互独立的判别方法
Rasearch on the non-independent investment decision making problem;非相互独立运输投资项目的模糊优选
3 main controllers are installed respectively in the 3 sections,and they are mutually independent as well as mutually related .3个工段分别安装3台控制主机，既相互独立，又相互关联。
Are acquisition and learning separate from or merged with each other?;习得与学知是相互独立还是相互融合?——评Krashen的习得—学知区分论
Outline the letter as separately numbered paragraphs.用一些相互独立的段落来描绘出信函的轮廓。
Some New Results on Independent Cycles and 2-Factor in Graphs;关于图中相互独立的圈和2-因子的新结果
Applications of covariance matrices to mutualindependence of random variable;协差阵在随机变量相互独立性中的应用
The independence between Boyle law and Joule law in non-relativistic thermodynamics非相对论热力学中玻意耳定律与焦耳定律的相互独立性
the relation between two different kinds of organisms that are interdependent; each gains benefits from the other.两种机体相互独立的关系；一物可从他物获得益处。
Ask users to pick exactly one item from a list of mutually exclusive options.要求用户从一列相互独立的选项中选择最恰当的项。
Two mutually exclusive pathways of lysine biosynthesis have been established.现已确定赖氨酸的生物合成有两条相互独立的途径。
Ask users to pick zero or more items from a list of independent options.请用户从相互独立选项列表中挑选，可以不选也可以多选。
The process of having I/O and computing operations proceed independently of one another but interleaved in their sharing of the memory.使输入输出和运算操作相互独立地进行，但交替分享内存的方法。
Students Comprehension on Independent Event;两所省重点中学高二学生对相互独立事件的理解
These three mechanisms, while independent, are not mutually exclusive.这三种机制虽然是互相独立的，但并不互相排斥。
Progress bars operate independently and( can be) simultaneously.进度条操作互相独立，可以是同步的。
Interaction between hole edge and line cracks in a thin plate薄板中孔边裂纹与独立裂纹的相互作用
