| 二维离散型随机变量相互独立 |
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| 引用本文： | 张卷美 李滨予. 二维离散型随机变量相互独立[J]. 焦作工学院学报, 1997, 16(1): 77-80 |
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| 作者姓名： | 张卷美 李滨予 |
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| 作者单位： | [1]焦作工学院基础部 [2]北京市经济管理干部学院 |
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| 摘 要： | 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）。其中Ｆ（ｘ，ｙ），ＦＸ（ｘ），ＦＹ（ｙ）分别为（Ｘ，Ｙ），Ｘ，Ｙ的分布函数。一般用等式Ｐ｛Ｘ＝ｘｉ，Ｙ＝ｙｊ｝＝Ｐ｛Ｘ＝ｘｉ｝Ｐ｛Ｙ＝ｙｊ｝进行判定，其中（ｘｉ，ｙｊ）为（Ｘ，Ｙ）所有可能取值，ｉ＝１，２，…；ｊ＝１，２，…；没有给出具体证明。本文给出二维离散型随机变量相互独立的定义及与这种判定方法等价的严格证明。
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| 关 键 词： | 二维离散型随机变量 分布函数 相互独立 |
Independence of Two Dimensional Random Variable |
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| Zhang Juanmei et al. //Dept. of Foundamental Courses,Jiaozuo Institute of Technology,Jiaozuo. Independence of Two Dimensional Random Variable[J]. Journal of Jiaozuo Institute of Technology(Natural Science), 1997, 16(1): 77-80 |
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| Authors: | Zhang Juanmei et al. //Dept. of Foundamental Courses Jiaozuo Institute of Technology Jiaozuo |
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| Affiliation: | Zhang Juanmei et al. //Dept. of Foundamental Courses,Jiaozuo Institute of Technology,Jiaozuo 454000 |
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| Abstract: | 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. The independence is generally decided with equation P{X=x i,Y=y j}=P{X=x i}P{Y=y j} , Where (x i,y j) are the values of (X, Y),i=1,2,…; j =1,2,…. Though there is no proof in any publications. The authors rigorously demonstrated that the definition of two dimensional random variable equals to the decision method. |
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| Keywords: | two dimensional random variable distribution function independence |
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