) Let X = (X1, X2, X3)' be distributed as N3(, ), where = (1,-1,2)' and...

  

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) Let X = (X1, X2, X3)' be distributed as N3(, ), where = (1,-1,2)' and 40-1 05 0 -1 0 2 Which of the following random variables are independent? Explain. (a) (1 mk) X1 and X2; (b) (1 mk) X1 and X3; (c) (1 mk) (X1, X3)' and X2; (d) (2 mk) (X1+ X2)/2 and X3; (e) (2 mk) X1 and X1 +3X2-2X3. ) Let X = (X1, X2, X3)' be distributed as N3(, ), where = (1,-1,2)' and 40-1 05 0 -1 0 2 Which of the following random variables are independent? Explain. (a) (1 mk) X1 and X2; (b) (1 mk) X1 and X3; (c) (1 mk) (X1, X3)' and X2; (d) (2 mk) (X1+ X2)/2 and X3; (e) (2 mk) X1 and X1 +3X2-2X3.