Exercise Solution 3.42
Construct the Cholesky matrix z of Σ,
and a matrix u with rows equal to orthonormal eigenvectors of :
We define the change of variables ~ N3(0,I) for X
Multiplying [s4] out:
We complete the squares for terms involving and to obtain
We have expressed Y as a linear polynomial of three independent random variables:
- ~ N(0,1).