estimated_standard_deviation
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| Both sides previous revisionPrevious revisionNext revision | Previous revisionNext revisionBoth sides next revision | ||
| estimated_standard_deviation [2016/06/23 18:57] – hkimscil | estimated_standard_deviation [2019/10/19 05:05] – hkimscil | ||
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| 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*} |
| </ | </ | ||
| 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] | ||
estimated_standard_deviation.txt · Last modified: 2023/09/13 11:00 by hkimscil