Mdm of the normal distribution

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Just starting to ask the question. Once this is worked out, it'll then be changed to a statement/proof page and marked as a theorem Alec (talk) 23:01, 24 November 2017 (UTC)

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Question

Let $X\sim$$\text{Nor}$$(\mu,\sigma^2)$, then:

• $$\mathbb{E}\big[\ \vert X-\mathbb{E}[X]\vert\ \big]\eq \int_{-\infty}^{+\infty}\big( \vert x-\mathbb{E}[X]\vert\!\ f_X(x)\big)\mathrm{d}x$$
  • $$\eq 2 \int_\mu^\infty\big( (x-\mathbb{E}[X])\!\ f_X(x)\big)\mathrm{d}x$$ - check this, hopefully reduces from here!