| 摘要: | 令S_{x,n}^2,S_{y,n}^2及S_{z,n}^2分表取自三獨立常態分布N({\mu}_x,{\sigma}_x^2),N({\mu}_y,{\sigma}_y^2)及N({\mu}_z,{\sigma}_z^2)之樣本變異數.當n為不小於2之整數時謝宗翰(2012)計算p(S_{x,n}^2>S_{y,n}^2)之值.當n為不小於3之奇數時謝宗翰(2012)計算P(S_{x,n}^2>S_{y,n}^2>S_{z,n}^2)之值.
本文用不同的計算方式來計算P(S_{x,n}^2>S_{y,n}^2)及P(S_{x,n}^2>S_{y,n}^2>S_{z,n}^2),
其結果適用於所有的偶數n.
Let S_{x,n}^2,S_{y,n}^2 and S_{z,n}^2 denote sample variances obtained from three independent normal distributions . Each sample has sample size n . Shieh (2012) calculated P(S_{x,n}^2>S_{y,n}^2) when n Greater than or equal 2 and P(S_{x,n}^2>S_{y,n}^2>S_{z,n}^2) when n Greater than or equal 3 is odd. In this paper , we calculate P(S_{x,n}^2>S_{y,n}^2) and P(S_{x,n}^2>S_{y,n}^2>S_{z,n}^2 by different methods and the results are valid for even n. |
