# Relatively Short Stat assignment Mostly dealing with Matrix's

Complete the assignment that was attached. I would highly prefer for it to be typed up but handwriting will be acceptable if its very legible.

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Statistics 344 –Review questions for Term Test 1 page 1 I Consider the matrices A, B, C.       − − =           =      = 011 111 , 1 1 0 0 2 3 , 102 24 CBA a) Compute A-1 b) Compute A + CB. c) Compute (B’B)-1. d) Compute (C’C)-1 B II Consider the matrix A 4 2 1 1 1 2 10 1 1 0 3 0 1 0 0 2 1 0 1 0 0 1 0 0 1 A −         −      =                        e) Compute A-1 f) Compute the determinant of A. III Consider the random vector 1 2 3 X x X X    =      which has the multivariate normal with mean vector 160 125 130 µ    =      and covariance matrix 40 20 15 20 20 10 15 10 20    Σ =      Determine 1. the marginal distribution of X1, X2. 2. the conditional distribution of X1, X2 given X3=105. 3. the conditional distribution of X1 given and X2= 100, X3=105. IV Consider the random vector              4 3 2 1 X X X X x which has the multivariate normal with mean vector              70 30 25 60  and covariance matrix              54302830 30211415 28142222 30152234 Determine 1. the marginal distribution of X1, X2 and X4. 2. the marginal distribution of X1, X2. 3. Determine the correlation of X1, X2. 4. the conditional distribution of X1, X2 and X3. given X4=75. 5. the conditional distribution of X1, X2 given X3=30, X4=75. 6. Determine the partial correlation of X1, X2 given X4=75 7. Determine the partial correlation of X1, X2 given X3=30, X4=75 page 2 yV. If is distributed N μ, V( ) , show that Q = y − μ( )′ V −1 y − μ( ) is distributed a χ2(p). yVI. If is distributed N (0,I), find E[y ′(I − X(X′X)-1 X′ )⋅ y] Stats 851 443 Take Home Final.pdf S344Test1.pdf Binder1.pdf S 344 Test 1 questions b S 344 Test 1 questions.pdf

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