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| − | <math>\mu = \mathcal{E}[x] = \int\limits_{- | + | <math>\mu = \mathcal{E}[x] =\int\limits_{-\infty}^{\infty} xp(x)\, dx</math> |
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Revision as of 16:01, 4 April 2013
Discriminant Functions For The Normal Density
Lets begin with the continuous univariate normal or Gaussian density.
$ f_x = \frac{1}{\sqrt{2 \pi} \sigma} \exp \left [- \frac{1}{2} \left ( \frac{x - \mu}{\sigma} \right)^2 \right ] $
for which the expected value of x is
$ \mu = \mathcal{E}[x] =\int\limits_{-\infty}^{\infty} xp(x)\, dx $
