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**Unformatted text preview: **X = " 2 1 # and S = " 10-2-2 10 # . Solution : We know P ( d 2 ( X , μ ) < c 2 ) = . 95 if c 2 = χ 2 2 ( . 05) = 5 . 99 , ( X-μ ) S n !-1 ( X-μ ) ≤ c 2 . eigenvectors of S n eigenvalues of S n : λ i n ( same as those of S ) ( eigenvalues of S : λ i ) u 1 = " . 707-. 707 # ( λ 1 = 12) λ 1 n = 12 78 u 2 = " . 707 . 707 # ( λ 2 = 8) λ 2 n = 8 78 1 2 3 4-1 1 2 3 μ 1 μ u X + half axis length = c s λ i n We are 95% conﬁdent that μ is in the ellip-soid centered at X = " 2 1 # with axes . 960 u 1 & . 784 u 2 . II.A-2...

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- Fall '08
- Staff
- Covariance, Normal Distribution, Variance, consistent estimator, multivariate statistical inference, IID Data