apricimo 8 Posted January 20, 2011 Share Posted January 20, 2011 (edited) In a book I am reading they list these steps and I don't understand the simplification... BTW u is a random variable and bar over u is the average for notation clearification [math] \begin{array}{l} \Delta u = u - \overline u \\ \overline {\Delta u} = \overline {(u - \overline u )} = \overline u - \overline u = 0 \\ \overline { < \Delta u > ^2 } = \sum\limits_{i = 1}^M {P(u_i } )(u_i - \overline u )^2 > 0 \\ \overline {(u_i - \overline u )^2 } = \overline {(u^2 - 2u\overline u + \overline u ^2 )} = \overline {u^2 } - 2\overline {uu} + \overline u ^2 \\ \end{array} [/math] and then they simplify to [math] \overline {(u_i - \overline u )^2 } = \overline {u^2 } - \overline u ^2 [/math] where did the middle term go? Edited January 20, 2011 by apricimo Link to post Share on other sites

D H 1371 Posted January 20, 2011 Share Posted January 20, 2011 [math]\aligned \overline{(u-\bar u)^2} &= \overline{u^2} - 2\bar u\,\bar u + \bar u^2 \\ &= \overline{u^2} - 2 \bar u^2 + \bar u ^2 \\ &= \overline{u^2} -\bar u^2\endaligned[/math] Link to post Share on other sites

apricimo 8 Posted January 20, 2011 Author Share Posted January 20, 2011 (edited) [math]\aligned \overline{(u-\bar u)^2} &= \overline{u^2} - 2\bar u\,\bar u + \bar u^2 \\ &= \overline{u^2} - 2 \bar u^2 + \bar u ^2 \\ &= \overline{u^2} -\bar u^2\endaligned[/math] ok... got it Edited January 20, 2011 by apricimo Link to post Share on other sites

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