6. Define a vector z as z = P'(x - $\mu$), where x is a random n x 1 vector with a normal density given by Eq. (10.6.2) and P is an orthogonal matrix of constants such that P'VP = D, a diagonal matrix. Show that

$$\phi(z'z) = \sum_{i=1}^n d_{ii}.$$

where $d_{ii}$ is the i-th diagonal element of D.