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--- estimated_standard_deviation [2016/06/23 18:56] – hkimscil
+++ estimated_standard_deviation [2017/12/11 09:41] – hkimscil
@@ Line 1: / Line 1: @@
-====== 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://www.qc.edu.hk/math/Advanced%20Level/Standard_deviation.htm \\
 우선, Expected value (기대값)와 Variance (분산)의 연산은 아래와 같이 계산될 수 있다.
-<WRAP box>
+<WRAP box 450px>
 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] &=& E[X] + E[Y] \\
-Var[aX] = a^{\tiny{2}} Var[X] \\
+Var[aX] &=& a^{\tiny{2}} Var[X] \\
-Var[X+Y] = Var[X] + Var[Y]
+Var[X+Y] &=& Var[X] + Var[Y]
-\end{eqnarray}
+\end{eqnarray*}
 </WRAP>