# 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:

\(\Sigma = \sigma^2 I\)