estimated_standard_deviation
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| Both sides previous revisionPrevious revisionNext revision | Previous revisionNext revisionBoth sides next revision | ||
| estimated_standard_deviation [2020/12/05 19:06] – [수학적 증명] hkimscil | estimated_standard_deviation [2021/11/27 18:56] – [Why n-1] hkimscil | ||
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| Line 11: | Line 11: | ||
| \begin{eqnarray*} | \begin{eqnarray*} | ||
| - | \hat{\sigma}^{2} | + | \hat{\sigma}^{2} |
| \end{eqnarray*} | \end{eqnarray*} | ||
| Line 487: | Line 487: | ||
| & = & \dfrac{1}{n} E \left[\sum{(X_{i}-\overline{X})^{2}} \right] \\ | & = & \dfrac{1}{n} E \left[\sum{(X_{i}-\overline{X})^{2}} \right] \\ | ||
| & = & \dfrac{1}{n} (n-1) \sigma^{2} \\ | & = & \dfrac{1}{n} (n-1) \sigma^{2} \\ | ||
| - | & = & (\dfrac{n-1}{n}) \sigma^{2} \\ | + | & = & \left(\dfrac{n-1}{n}\right) \sigma^{2} \\ |
| \end{eqnarray*} | \end{eqnarray*} | ||
estimated_standard_deviation.txt · Last modified: 2023/09/13 11:00 by hkimscil