[SOLVED] proving a theorem regarding expected value

**takeyourmark** · March 7th 2009, 11:14 AM

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

**Plato** · March 7th 2009, 11:22 AM

Originally Posted by takeyourmark

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

$E\left( {\left[ {X - E(X)} \right]^2 } \right) = E\left( {X^2 - 2XE\left( X \right) + E^2 \left( X \right)} \right)$ $= E\left( {X^2 } \right) - 2E\left( X \right)E\left( X \right) + E^2 \left( X \right) = E\left( {X^2 } \right) - E^2 \left( X \right)$

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[SOLVED] proving a theorem regarding expected value

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