# Independent and identically distributed variables

## Identically Independently Distributed variables (IID)

### IID

#### Identically distributed

$$x$$ is identically distributed to $$y$$ if:

$$\forall i (\exists x_i \rightarrow P(x_i)=P(y_i))$$

#### Covariance matrix of IID variables

For IID varaibles, the covariance matrix is:

$$\Sigma = \sigma^2 I$$