(New page: = Discriminant Functions For The Normal Density = ---- Lets begin with the continuous univariate normal or Gaussian density. <div style="margin-left...) |
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<math>f_x = \frac{1}{\sqrt{2 \pi} \sigma} \exp \left [- \frac{1}{2} \left ( \frac{x - \mu}{\sigma} \right)^2 \right ] </math> | <math>f_x = \frac{1}{\sqrt{2 \pi} \sigma} \exp \left [- \frac{1}{2} \left ( \frac{x - \mu}{\sigma} \right)^2 \right ] </math> | ||
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| + | for which ''the expected value'' of ''x'' is | ||
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| + | <math> /mu = \varepsilon \left [x \right] = \int\limits_{-/infty}^{/infty} xp(x)\, dx</math> | ||
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Revision as of 15:58, 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 = \varepsilon \left [x \right] = \int\limits_{-/infty}^{/infty} xp(x)\, dx $
