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Unformatted text preview: Let X = X 1 , where X 1 and X 2 are subvectors of X. Suppose X has multivariate X 2 normal distribution with mean value vector and covariance matrix: m = m 1 , and Σ = Σ 11 Σ 12 ( Σ 12 = Σ 21 T ). m 2 Σ 21 Σ 22 Then, given X 2 = x 2 , the conditional vector (X 1  X 2 = x 2 ) has jointly normal distributions with parameters: m 12 (x 2 ) = m 1 + Σ 12 Σ − 22 1 (x 2 − m 2 ) (2) − 1 T Σ 12 (x 2 ) = Σ 11 − Σ 12 Σ 22 Σ 12 Notice again that Σ 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 Σ ....
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 Spring '05
 GeorgeKocur

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