estimated_standard_deviation
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estimated_standard_deviation [2016/03/14 02:25] – hkimscil | estimated_standard_deviation [2017/12/11 09:41] – hkimscil | ||
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- | ====== | + | ====== |
+ | Why we use n-1 instead of n in getting standard deviation \\ | ||
http:// | http:// | ||
우선, Expected value (기대값)와 Variance (분산)의 연산은 아래와 같이 계산될 수 있다. | 우선, Expected value (기대값)와 Variance (분산)의 연산은 아래와 같이 계산될 수 있다. | ||
- | <WRAP box> | + | <WRAP box 450px> |
X,Y are Independent variables. | X,Y are Independent variables. | ||
- | \begin{eqnarray} | + | \begin{eqnarray*} |
- | E[aX] = a E[X] \\ | + | E[aX] &=& a E[X] \\ |
- | E[X+Y] = E[X] + E[Y] \\ | + | E[X+Y] |
- | Var[aX] = a^{\tiny{2}} Var[X] \\ | + | Var[aX] |
- | Var[X+Y] = Var[X] + Var[Y] | + | Var[X+Y] |
- | \end{eqnarray} | + | \end{eqnarray*} |
</ | </ | ||
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$ E[S^2] = \displaystyle \frac{(n-1)\sigma^2}{n} * \frac{n}{n-1} = \sigma^2 $ | $ E[S^2] = \displaystyle \frac{(n-1)\sigma^2}{n} * \frac{n}{n-1} = \sigma^2 $ | ||
- | {{tag>" | + | {{tag>" |
estimated_standard_deviation.txt · Last modified: 2023/09/13 11:00 by hkimscil