[X1 X2 X3]^T ~ N_3(mu,sigma) if it matters...
Suppose [X1 X2 X3]^T ~ N(mu,sigma) where mu = [1,2,3] and sigma = [(1,2,2),(2,3,2),(2,2,5)]. I want to find a vector a such that X2 and X2 -a^T*[X1,X3]^T are independent. To do this do we start by finding a1 and a2 (froma) such that cov(X2,X2-a1*X1 -a3*X3) = 0? If so, can someone work through the problem from there and find a, cheers.