χ2乗分布に関する定理の簡単な証明

抄録

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.