6 suppose the energy function of a 3d gaussian vector of mean zero is

Search for question

Question

6. Suppose the energy function of a 3D gaussian vector of mean zero is given by:
E(x, y, z) = ax² + by² + cz² + dxy + exz + fyz
Show that the conditional distribution of X assuming that Y = y and Z = z is a 1D gaussian
of variance 1/(2a) and mean:
(A) 4abc-cd2-be² + def - af²
(B) 4abc+cd2+ be² - def + af²
(C) Can't be computed. Not enough information.
(D) 2abc-cd2-be² + def - af²
(E) 2abccd2+ be² - def + af²