Question: QUESTION 1 Let X = (X1. X2, X3, X, ) be a normal random vector with 0 0 0 040 0 E(X) = and Var(X)

QUESTION 1 Let X = (X1. X2, X3, X, ) be a normal random vector with 0 0 0 040 0 E(X) = and Var(X) = 19 2 N 4 Given the following linear combinations of X: Y1 = X1 +X 2 Y2 = 2X1 + X3 Y3 - X1 - XA a) Express Y in matrix form. (Hint: Y = AX) (2 marks) b) Calculate the mean vector and covariance matrix of Y. (5 marks) c) Are (Y1 , Y2) and Y; independent? Justify your answer. (3 marks) d) Obtain the correlation matrix of Y

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