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Thread: Can you prove to me that the 2nd central moment = 2nd raw moment?

  1. #1
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    Can you prove to me that the 2nd central moment = 2nd raw moment?

    How does E[(X-mu)^2] = E[X^2]-(E[X])^2 ?
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  2. #2
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    Re: Can you prove to me that the 2nd central moment = 2nd raw moment?

    If we factor the first component of the equation, we get:

    X^2 - 2muX + mu^2
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  3. #3
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    Re: Can you prove to me that the 2nd central moment = 2nd raw moment?

    $\begin{align*}
    &E[(X-\mu)^2] = \\

    &E[X^2 - 2 X \mu + \mu^2] = \\

    &E[X^2] - 2\mu E[X] + \mu^2 = \\

    &E[X^2] - 2 \mu^2 + \mu^2 = \\

    &E[X^2] - \mu^2 = \\

    &E[X^2] - \left(E[X]\right)^2

    \end{align*}$
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