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Math Help - [SOLVED] proving a theorem regarding expected value

  1. #1
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    [SOLVED] proving a theorem regarding expected value

    prove that  E[X-E(X)]^2 = E(X^2)-[E(X)]^2
    Last edited by Jhevon; March 7th 2009 at 02:11 PM.
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  2. #2
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    Quote Originally Posted by takeyourmark View Post
    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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