Normal Distribution
Notation:
$X \sim \mathcal{N}(\mu, \sigma)$
Probability Density Function:
$f(x)=\dfrac{1}{\sqrt{2\pi\sigma^2}} e^{-
\frac{\left(x-\mu\right)^2}{2\sigma^2}}$
where:
- $\mu \in \mathbb{R}$ mean
- $\sigma > 0$ standard deviation
- $x \in \mathbb{R}$
Mean:
$\mathrm{E}[X]=\mu$
Variance:
$\mathrm{Var}[X]=\sigma^2$
Alternative Parameterizations:
-
$\mathcal{N}(\mu, \sigma^2)$ - where $\sigma^2$ is the variance (squared standard deviation).
-
$\mathcal{N}(\mu, \tau)$ - where $\tau$ is the precision ($\tau = 1/\sigma^2$).
References:
-
Normal Distribution - Wikipedia
-
Normal Distribution - Wolfram MathWorld