if X = (X₁, X₂, X3) is a trivanate random vanable with vector mean M' = (5 3 4) and matrix vanance E= 2 and vectors g = (120) and b' = (20-1) 1 1 0 for count: a. Var (ax) b. Cov (axb'x) C. E (abx) ( 2 1 O 1 2
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- Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.4. Let X'= (X₁,..., Xn) be an n-dimensional random vector whose covariance matrix exists. Let A be an m x n matrix of constants. Then Cov(AX) = ACov(X)A'. True or false, give reasoning.Express the model Y₁ = Bo + Bixi + B₁x² + €i i=1,2,..., 5 where the &; have mean zero, variance o² and are uncorrelated, as a general linear model in matrix form by specifying Y, X, 3 and e.
- Find the least-squares line given the matrix products AT A = 590.4 6895.2 ать = - [50 Y Ex: 1.2 + Ex: 1.2 X 4 37 37 531 andIf x ER" is a column vector (i.e. an n x1 matrix), then In-2xx' is always a symmetric matrix. True FalseSuppose A is the 3 by 3 matrix ones(3, 3) of all ones. Find two independent vec- tors x and y that solve Ax = 0 and Ay 0. Write that first equation Ax = 0 (with numbers) as a combination of the columns of A. Why don't I ask for a third independent vector with Az = 0? -
- Now we can solve for x in the normal equations, using the inverse matrix and simplified vector that we previously found. Find the least squares solution of Ax = b. ATAX = ATb (ATA 11 4 134 67 X = 4 9 67 67 X =3. Consider the vector B1 B = B2 with variance-covariance matrix Var(B,) Var(ß) = ( Cov(B1, B2) Cov (β, β ) Var(8,) ) and the matrix 3 -1 A = 1 Show – for this example – that Var(AB) = AVar(B)A'.