Exercise Solution 5.7
We construct an N3(0,I) pseudorandom vector x from the U3((0,1)3) pseudorandom vector [5.47]:
We calculate the Cholesky matrix k for Σ, as described in Section 2.7. We obtain:
Applying [5.46] to [s1], we obtain the desired pseudorandom vector:
See spreadsheet for the actual computations.