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Unformatted text preview: N ( , ) where = 1 /n ( n-1) /n-1 /n -1 /n-1 /n ( n-1) /n -1 /n . . . . . . . . . . . . . . .-1 /n-1 /n ( n-1) /n . By a theorem from last lecture (Theorem V.7.2), we conclude from the form of that X and ( X 1-X, . . . , X n-X ) are independent normal random vectors. It now follows from the transformation theorem (Theorem I.2.1 on page 23) that since X = ( X 1-X, . . . , X n-X ) and X are independent, so too are X and X X = n X i =1 ( X i-X ) 2 . This now implies that X and S 2 are independent....
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