=3.16. Let V be a vector random variable with mean vector E(V)E(V – μν)(V – μν)' = Σy. Show that E(VV') = Σν + μνμίν.-My and covariance matrix

Given information E(v)=μv,Σv=E(v−μv)(v−μv)′

Answered: 16. Let V be a vector random variable…

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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Consider a random process X(t) = A cos o t where a' is a constant and A is a random variable uniformly distributed over (0, 1). Find the auto correlation and covariance of X(t).
2 Let B be the (k + 1) × 1 vector of OLS estimates. (i) Show that for any (k + 1) × 1 vector b, we can write the sum of squared residuals as SSR(b) = û'û + (ß – b)'X'X(ß – b). {Hint: Write (y – Xb)'(y – Xb) = [û + X(ß – b)]'[û + X(ß – b)] and use the fact that X'û = 0.} Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). hat any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. (ii) Explain how the expression for SSR(b) in part (i) proves that B uniquely minimizes SSR(b) over all possible values of b, assuming X has rank k + 1.
X is multivariate Gaussian with "X - [6 8]and C₁ n 608 = and covariance matrix of Y 1 = X1 X2 2 = x1 + x₂ - 2x3 Y3 = x1 + x3 1/2 1/4 1/3 1/4 2 2/3 1/3 2/3 1 = [y₁ У1 У2 уз y3]. Find the mean vector where
Four data points, (0,1), (1,4), (2,2), and (3,3), were collected in an experiment. The DFT of [1, 4, 2, 3] is [5, - - i, -2, - +zi]. Let f (t) + 늑1. Let f (t) = a + b cos( nt) + c sin(÷ Tt) + d cos(at) be the trig interpolation function that passes through the four data points. What is the value of the coefficient d?
A zero mean vector [B]2x1 is unitarily 2X1 1 13 transformed. Given A = 2 1 В, -1 3 1 and Ru: 0 < p < 1. р 1 Obtain covariance matrix RA. Also obtain `A' correlation between A(0) and A(1), if p=0.95.
Let X.,X,"(4,0²). Consider the fotlowing estimators of u A, =(X+ Xs + X, + X10) A = (X2+ X, +Xp). Then (a) A, is more efficient than Az (b iz is more efficient than i (e) Can't deside (d) None
5. Given that G(x, y) = (x² + 1, y²) and F(u, v) = (u + v, v²), compute the Jacobian derivative matrix of F(G(x, y)) at the point (x, y) = (1, 1).

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16. Let V be a vector random variable with mean vector E(V): E(V – μν)(V – μν)΄ = Σy. Show that E(VV') = Σν + μνμν. - = M, and covariance matrix