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Unformatted text preview: âˆˆ N ( , Î›) where Î› = 1 /n Â·Â·Â· ( n1) /n1 /n Â·Â·Â·1 /n1 /n ( n1) /n Â·Â·Â·1 /n . . . . . . . . . . . . . . .1 /n1 /n Â·Â·Â· ( n1) /n . By a theorem from last lecture (Theorem V.7.2), we conclude from the form of Î› that X and ( X 1X, . . . , X nX ) are independent normal random vectors. It now follows from the transformation theorem (Theorem I.2.1 on page 23) that since X = ( X 1X, . . . , X nX ) and X are independent, so too are X and X X = n X i =1 ( X iX ) 2 . This now implies that X and S 2 are independent....
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 Fall '08
 MichaelKozdron
 Statistics, Probability, Standard Deviation, Variance, xj, Cov Xj

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