Normal distribution

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p(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\!\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)

The bell curve: fully described by a mean and a spread, and the shape that sums of many independent effects converge to. Its log is a plain squared error, which is why Gaussian assumptions and L2 losses keep turning up together.

Symbols

$\mu$: The mean, where the curve is centred.
$\sigma$: The standard deviation, how wide it is.
$\exp$: The exponential function.

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Normal distribution

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