prove that $\displaystyle E[X-E(X)]^2 = E(X^2)-[E(X)]^2 $

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- Mar 7th 2009, 10:14 AMtakeyourmark[SOLVED] proving a theorem regarding expected value
prove that $\displaystyle E[X-E(X)]^2 = E(X^2)-[E(X)]^2 $

- Mar 7th 2009, 10:22 AMPlato
$\displaystyle E\left( {\left[ {X - E(X)} \right]^2 } \right) = E\left( {X^2 - 2XE\left( X \right) + E^2 \left( X \right)} \right)$$\displaystyle = E\left( {X^2 } \right) - 2E\left( X \right)E\left( X \right) + E^2 \left( X \right) = E\left( {X^2 } \right) - E^2 \left( X \right)$