Normal Distribution

$$f(x)=\frac{1}{\sigma \sqrt{2\pi }}\exp \left(-\frac{(x-\mu {)}^2}{2{\sigma }^2}\right),x\in \mathbb{R}$$

Expected Value

$$\mathbb{E}[X]=\mu$$

Variance

$$\mathrm{Var}(X)={\sigma }^2$$