### 3d) [ON PAPER] A Reparametrization ### Your work in Parts 2 and 3 has shown that $$ f_\mathbf{V}(\mathbf{v}) ~ = ~ \frac{1}{(\sqrt{2\pi})^2 \sqrt{\det(\boldsymbol{\Sigma}_\mathbf{V})} } \exp \big{(} -\frac{1}{2} \mathbf{v}^T \boldsymbol{\Sigma}_\mathbf{V}^{-1} \mathbf{v} \big{)} $$ The joint density has been expressed in terms of the parameter $\boldsymbol{\Sigma}$, the covariance matrix. We say that $\mathbf{V}$ has the **centered bivariate normal distribution with covariance matrix $\boldsymbol{\Sigma}_\mathbf{V}$**. Confirm that the formula at the end of Part 1 is a special case of this one. This way of expressing the joint density in terms of the covariance matrix extends to higher dimensions. The dimension 2 gets replaced by the new dimension $n$, but other than that, the formula remains exactly the same