Hi,

I think that there is a typo in the answer of the question 3.54.

If Z_1 ~ N(0,1), then W_1 = a Z_1 ~ N(0,a^2).

Besides, considering that (X,Y) is a gaussian vector with mean 0, we should have:

E[X|2X+Y] = E[X(2X+Y)]/E[(2X+Y)^2] x (2X+Y)

with E[X(2X+Y)] = 2a + rho sqrt(ab)

E[(2X+Y)^2] =4a + b + 4 rho sqrt(ab)

Regards.