Unformatted text preview: âŽ£ X 2 âŽ¦ normal distribution with mean value vector and covariance matrix: âŽ¡ m 1 âŽ¤ m = âŽ¢ âŽ¥ , and = Î£ âŽ¡Î£ 11 Î£ 12 âŽ¤ ( Î£ 12 = Î£ 21 T ). âŽ¢ âŽ£ m 2 âŽ¦ âŽ£ Î£ 21 Î£ 22 âŽ¦ âŽ¥ Then, given X 2 = x 2 , the conditional vector (X 1  X 2 = x 2 ) has jointly normal distributions with parameters: âˆ’ 1 âŽ§ m 12 (x 2 ) = m 1 Î£ + 12 Î£ (x âˆ’ m 2 ) âŽª 22 2 âŽ¨ (2) T âŽª Î£ 12 (x ) Î£ = 11 Î£ âˆ’ 12 Î£ âˆ’ 1 Î£ 2 22 12 âŽ© Notice again that Î£ 12 does not depend on x 2 . As for the scalar case, Eq. 2 may be used in approximation when X does not have multivariate normal distribution or when the distribution of X is not known, except for the mean vector m and covariance matrix Î£ ....
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 Fall '07
 DonHill

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