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2.1.6 The Normal density function

Definition 10   A continuous random variable $ X$ is said to have a Normal (or Gaussian) density function $ f_{X}$ with mean $ \mu$ and variance $ \sigma^2$ if:

$\displaystyle f_X(x) = \frac{1}{\sqrt{2 \pi \sigma^2}} \mathrm{e}^{-\frac{(x-\mu)^2}{2\sigma^2}} $

This is summarized by writing:

$\displaystyle X \approx N(\mu,\sigma^2) $

This is the classic bell shaped curve (see this handout).


Eran Borenstein