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QuoteOriginally posted by: SteilermeierCan anyone tell me if (I have used Var(X)=a^2 and Var(Y)=b^2)\frac{2a^2-\rho a b-b^2}{\sqrt{4a^2+b^2+4 \rho a b}} * (2X + Y)is the right answer to question 1)? If not, could you please provide a book recommendation. Thanx!Why \sqrt ?Since U=X-Y and V=2X+Y are jointly gaussian then E(U|V) = \beta + \alpha VE(E(U|V)) = E(U) ---> \beta = 0E(V E(U|V)) = E(UV) ---> \alpha (4a^2 + 4ab\rho + b^2) = 2a^2 - ab\rho - b^2 (see EscapeArtist999)

For 1, I think a quick way not to use a formula in note is to this: (assume a,b are variance) i). Find a combination X+w Y is orthogonal to 2X+Y. i.e. 0=E[(X+w Y)(2X+Y)]=2a+(2+w)\rho\sqrt(ab)+w b. ii). Expand X+Y into basis of s1(X+wY)+s2(2X+Y) and expectation is E[X+Y]=s2(2X+Y)