Let X = (X₁, . . . , Xn) denote an (n × 1) vector of independent random variables Xi∼ N (0, 1), i = 1, . . . , n. Let A = [aij] denote an (m × n) matrix, and define a random vector Y = (Y₁, . .. , Ym) asY = AX.Show that Cov(Yi, Yj)Which of the following lines is a valid argument?See attached pic (X1, ..., Xn)' denote an (n x 1) vector of independent random variables X; ~N(0, 1),[aij] denote an (m x n) matrix, and define a random vector Y = (Y1,..., Ym) asLet Xi = 1, ... , n. Let A =Y = AX.Show that Cov(Y;,Y;) = £k=1 aikajk·Which of the following lines is a valid argument? Let RHS= L=1 aikajk.(a) Cov(Y;, Y;) = Var(Y;)Var(Y;)Var(Y:)Var(Y;)Corr(Y;,Y;)RHS(b) Cov(Y;, Y;) == RHS( c) Cov (Y, Y) - (Σ, an)(Σ, α)Σ α-(Σ αk)? = RHS(d) Cov(Y;,Y;)(Ex aik)(Ee aje) = Ek a – (Ex aik)² = RHSY;)E(Y;Y;) = Ek aikajkE(Xf)+ 2Ek

N(0, 1), (X1, ..., Xn)' denote an (n x 1) vector of independent random variables X; i = 1,..., n. Let A = [a;j] denote an (m x n) matrix, and define a random vector Y = (Y1,... , Y,m) as Let X = 2. Y = AX. Show that Cov(Y;,Y;) = Ek=1 aikajk· Which of the following lines is a valid argument? Let RHS=E-1aikajk. k3D1 (a) Cov(Y;, Y;) = Var(Y;)Var(Y;) = RHS Var(Y;) Var(Y,) (b) Cov(Yi, Y;) = Corr(Y,,Y;) = RHS (c) Cov(Y;, Y;) = (Ex aik)(Ee aje) = Ek až% – (Ex dik)² = RHS (d) Cov(Y;, Y;) = E(Y;Y;) = Ek aikajkE(X})+2Ek

N(0, 1), (X1, ..., Xn)' denote an (n x 1) vector of independent random variables X; i = 1,..., n. Let A = [a;j] denote an (m x n) matrix, and define a random vector Y = (Y1,... , Y,m) as Let X = 2. Y = AX. Show that Cov(Y;,Y;) = Ek=1 aikajk· Which of the following lines is a valid argument? Let RHS=E-1aikajk. k3D1 (a) Cov(Y;, Y;) = Var(Y;)Var(Y;) = RHS Var(Y;) Var(Y,) (b) Cov(Yi, Y;) = Corr(Y,,Y;) = RHS (c) Cov(Y;, Y;) = (Ex aik)(Ee aje) = Ek až% – (Ex dik)² = RHS (d) Cov(Y;, Y;) = E(Y;Y;) = Ek aikajkE(X})+2Ek

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

100%

Let X = (X₁, . . . , Xn) denote an (n × 1) vector of independent random variables Xi∼ N (0, 1), i = 1, . . . , n. Let A = [aij] denote an (m × n) matrix, and define a random vector Y = (Y₁, . .. , Ym) as
Y = AX.

Show that Cov(Yi, Yj)

Which of the following lines is a valid argument?

See attached pic

(X1, ..., Xn)' denote an (n x 1) vector of independent random variables X; ~
N(0, 1),
[aij] denote an (m x n) matrix, and define a random vector Y = (Y1,..., Ym) as
Let X
i = 1, ... , n. Let A =
Y = AX.
Show that Cov(Y;,Y;) = £k=1 aikajk·
Which of the following lines is a valid argument? Let RHS= L=1 aikajk.
(a) Cov(Y;, Y;) = Var(Y;)Var(Y;)
Var(Y:)Var(Y;)
Corr(Y;,Y;)
RHS
(b) Cov(Y;, Y;) =
= RHS
( c) Cov (Y, Y) - (Σ, an)(Σ, α)Σ α-(Σ αk)? = RHS
(d) Cov(Y;,Y;)
(Ex aik)(Ee aje) = Ek a – (Ex aik)² = RHS
Y;)
E(Y;Y;) = Ek aikajkE(Xf)+ 2Ek<e aikajlE(X½X¢)
(e) none of these

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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