# Normal Distribution#

The normal (or Gaussian) distribution is a very common continuous probability distribution in probability theory.

Parameters
Notation $$\mathcal N(μ, σ^2), μ ∈ \R, σ > 0$$
Mean $$μ$$
Variance $$σ^2$$
PDF $$f_X (x) = \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{(x-\mu)^2}{2 \sigma^2}}$$, $$x ∈ \R$$

## Probability Density#

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

with the mean $$\mu$$, the standard deviation $$\sigma$$.

## Properties#

• It is symmetric around the point $$x=\mu$$ which is at the same time the mode, the median and the mean of the distribution.
• The area under the curve and over the x-axis is equal to one.