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estimated_standard_deviation

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 estimated_standard_deviation [2017/12/11 09:41]hkimscil estimated_standard_deviation [2019/10/19 04:35] (current)hkimscil Both sides previous revision Previous revision 2019/10/19 04:35 hkimscil 2017/12/11 09:41 hkimscil 2016/06/23 18:57 hkimscil 2016/06/23 18:56 hkimscil 2016/03/14 02:25 hkimscil 2016/03/14 01:20 hkimscil 2016/03/07 00:43 hkimscil 2016/03/07 00:43 hkimscil 2016/03/06 17:17 hkimscil 2016/03/06 15:39 hkimscil 2016/03/06 15:36 hkimscil 2016/03/06 15:21 hkimscil 2016/03/06 15:03 hkimscil 2016/03/06 15:02 hkimscil 2016/03/06 15:00 hkimscil created 2019/10/19 04:35 hkimscil 2017/12/11 09:41 hkimscil 2016/06/23 18:57 hkimscil 2016/06/23 18:56 hkimscil 2016/03/14 02:25 hkimscil 2016/03/14 01:20 hkimscil 2016/03/07 00:43 hkimscil 2016/03/07 00:43 hkimscil 2016/03/06 17:17 hkimscil 2016/03/06 15:39 hkimscil 2016/03/06 15:36 hkimscil 2016/03/06 15:21 hkimscil 2016/03/06 15:03 hkimscil 2016/03/06 15:02 hkimscil 2016/03/06 15:00 hkimscil created Line 118: Line 118:  \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] ​