## 5.5 The normal distribution (continuous)

Definition 5.3 (Normal distribution) The normal distribution with mean $$\mu$$ and variance $$\sigma^2$$ has the PDF $f_X(x) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left\{ -\frac{(x-\mu)^2}{2\sigma^2}\right\}\qquad\text{for -\infty<x<\infty}$ for $$-\infty<\mu<-\infty$$ and $$\sigma^2>0$$.