# Normal distributions

## Outline

### Topics

- Quick review of the normal distribution.
- Different parameterizations.

### Rationale

The normal distribution is often used in Bayesian analysis when one needs a prior over an unknown \(x\) such that \(x \in (-\infty, \infty) = \mathbb{R}\).

## Examples of normal densities

## Parameterizations

- There are
**different conventions**to measure the spread.- Standard deviation \(\sigma\).
- Variance, \(\sigma^2\).
- Precision, \(\tau = 1/\sigma^2\).

**Keep that in mind**as different languages will use different conventions!- Standard deviation is the most intuitive:
- it is the width of the bell,
- the only one that has the same units as \(x\) (e.g. if \(x\) is in meters, so is \(\sigma\)).