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normal_distribution [2015/11/13 17:15] nikolaj created |
normal_distribution [2015/11/30 11:06] nikolaj |
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- | ===== Normal Distribution ===== | + | ===== Normal distribution ===== |
==== Function ==== | ==== Function ==== | ||
| @#FF9944: definition | @#FF9944: $f: {\mathbb C}\times{\mathbb C}\times{\mathbb C}\setminus\{0\}\to{\mathbb C}$ | | | @#FF9944: definition | @#FF9944: $f: {\mathbb C}\times{\mathbb C}\times{\mathbb C}\setminus\{0\}\to{\mathbb C}$ | | ||
- | | @#FF9944: definition | @#FF9944: $f(x, \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi} }{\mathrm e}^{ -\frac{(x-\mu)^2}{2\sigma^2}}$ | | + | | @#FF9944: definition | @#FF9944: $f(x, \mu, \sigma) = \dfrac{1}{\sigma\sqrt{2\pi} }{\mathrm e}^{ -\dfrac{(x-\mu)^2}{2\sigma^2}}$ | |
----- | ----- | ||
=== Discussion === | === Discussion === | ||
+ | People also like to write | ||
+ | |||
+ | ${\mathcal N}(\mu, \sigma) := \lambda x.\,f(x,\mu, \sigma)$ | ||
+ | |||
=== Theorems === | === Theorems === | ||
=== Reference === | === Reference === | ||
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----- | ----- | ||
- | === Context === | + | |
- | [[Function integral on ℝⁿ]], [[Complex exponents with positive real bases]] | + | |
=== Requirements === | === Requirements === | ||
[[Exponential function]] | [[Exponential function]] |