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**Unformatted text preview: **is positive? (20) 2. Exercise 5.4.8 3. Suppose X γ (c, d) and Z X = x N K ( θ , x-1 Ω ), where c > 0, d > 2, θ is a K×1 vector and Ω is a K×K positive definite matrix (all assumed known). Define Q = X(Z AZ), where A is a known K×K positive definite matrix. (15) (a) Find E(Q). (15) (b) Find Var(Q). [Hint: consider Exercise 3.4.35(b).] 2 Σ 1 ρ yx ρ yz ρ yx 1 ρ xz ρ yz ρ xz 1 . 4. Suppose Y, X and Z have a trivariate normal distribution with zero means and covariance matrix Define U = Y - ρ yx X. (10) (a) Find the conditional distribution of U, given X and Z. (10) (b) Is U mean-independent of X? (10) (c) Is U mean-independent of Z?...

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- Fall '10
- DaleJ.POIRIER
- Economics, Econometrics, Variance, Probability theory, Covariance matrix, Multivariate normal distribution, positive definite matrix