χ2乗分布に関する定理の簡単な証明  [in Japanese] An Easy Proof of a Theorem on χ-square Distributions  [in Japanese]

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Author(s)

Abstract

In the present paper, the auther gives an easy proof of the following theorem from the educational viewpoint for general students. When independent random variables $X_1,X_2,X_3,\ldots,X_n$(\thinspace$n$ is a natural number greater than 1\thinspace)are distributed according to one normal distribution with standerd deviation $\sigma$\thinspace, the random variable $\frac1{\sigma^2}\sum_{k=1}^n\bigl(X_k-\overlineX\bigr)^2$ where $ \overline X=\frac1n\sum_{k=1}^nX_k $ is distributed according to the χ-square distribution with $n-1$ degrees of freedom.

Journal

  • Journal of National Institute of Technology, Toyota College

    Journal of National Institute of Technology, Toyota College 44(0), 111-114, 2012

    National Institute of Technology, Toyota College

Codes

  • NII Article ID (NAID)
    110009277997
  • NII NACSIS-CAT ID (NCID)
    AN00176161
  • Text Lang
    JPN
  • Journal Type
    大学紀要
  • ISSN
    0286-2603
  • NDL Article ID
    023777609
  • NDL Call No.
    Z22-583
  • Data Source
    NDL  NII-ELS  J-STAGE 
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