The "first central moment" of a real-valued function(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\mu_1 \equiv \int_{-\infty}^\infty (x - \mu) f(x)\,dx = 0[/tex]

where

[tex]\mu \equiv \int_{-\infty}^\infty x\, f(x)\,dx[/tex]

so we have

[tex]\int_{-\infty}^\infty (x - \left ( \int_{-\infty}^\infty x\, f(x)\,dx \right ) ) f(x)\,dx = 0[/tex]

Intuitively, it seems to make sense, but how do we manipulate those integrals to prove this equality?

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# First central moment

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