estimated_standard_deviation
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estimated_standard_deviation [2016/06/23 18:56] – hkimscil | estimated_standard_deviation [2019/10/19 05:05] – hkimscil | ||
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- | ====== Why n-1 (Why we use n-1 instead of n in getting standard deviation) ====== | + | ====== Why n-1 ====== |
+ | 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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$$ | $$ | ||
\begin{align*} | \begin{align*} | ||
- | Var [X + Y] & = E[(X^2 + 2XY + Y^2)] - (a^2 - 2ab - b^2) \\ | + | Var [X + Y] & = E[(X^2 + 2XY + Y^2)] - (a^2 + 2ab - b^2) \\ |
& = E[X^2] - a^2 + E[Y^2] - b^2 \\ | & = E[X^2] - a^2 + E[Y^2] - b^2 \\ | ||
& = Var[X] + Var[Y] | & = Var[X] + Var[Y] |
estimated_standard_deviation.txt · Last modified: 2023/09/13 11:00 by hkimscil