### Covariance

We can compute the covariance between the two vectors $z^{(1)}$ and  $z^{(2)}$.

$$\textrm{cov}(z^{(1)},z^{(2)}) = \frac{1}{n}\sum_{i=1}^n (z^{(1)}_i-\bar{z}^{(1)})(z^{(2)}_i-\bar{z}^{(2)})$$

where $\bar{z}^{(j)}$ is the mean of the variable $z^{(j)}$ with $j=1,2$.