Mathematics · Probability and Statistics

Let n > 2 and 0 π 2 be fixed. Let X 1 , ..., X n be i.i.d. normal random variables with mean zero and variance σ 2 > 0. For i = 1, ..., n, define Y 2i-1 = X i cos(θ) and Y 2i = X i sin(θ). Further, let Z T = (Y 1 , Y 2 , ..., Y 2n ) and V T = (X 1 , Y 1 , Y 2 , X 2 , Y 3 , Y 4 , ..., X n , Y 2n-1 , Y 2n ). Which of the following statements is NOT correct?