| 两种不同抽样方式下样本均值的数学期望和方差的比较 |
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| 引用本文： | 刘淑华. 两种不同抽样方式下样本均值的数学期望和方差的比较[J]. 长春大学学报, 2012, 0(8): 983-985 |
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| 作者姓名： | 刘淑华 |
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| 作者单位： | 长春理工大学光电信息学院 |
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| 摘 要： | 给出了在有放回抽样时，样本均值的数学期望和方差的计算结果；同时通过引理的证明给出了在无放回抽样方式下，样本均值的数学期望和方差的结果。从而说明了在抽样方式不同的情况下，样本均值的数学期望相同，但方差却是不同的，但是，当样本容量n很大时，则两者的差别是不大的；当n趋于无穷大时，这两者就没有区别了。
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| 关 键 词： | 总体 样本 样本均值 样本方差 |
Comparison of Mathematical Expectation and Variance of Sample Mean by Means of Two Different Sampling Methods |
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| LIU Shu-hua. Comparison of Mathematical Expectation and Variance of Sample Mean by Means of Two Different Sampling Methods[J]. Journal of Changchun University, 2012, 0(8): 983-985 |
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| Authors: | LIU Shu-hua |
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| Affiliation: | LIU Shu-hua(College of Optical and Electronical Information,Changchun University of Science and Technology,Changchun 130022,China) |
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| Abstract: | This paper gives the calculation results of mathematical expectation and variance of sample mean in sampling scheme with replacement,at the same time,it presents the results of mathematical expectation and variance of sample mean in sampling scheme without replacement by using lemmas.So we can prove that the mathematical expectation of sample mean is same while the variance is different in different patterns of sampling.But when the sample size n is very large,the difference is slim and when the sample size n tends to infinite,the difference is little. |
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| Keywords: | overall sample sample mean sample variance |
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