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

See similar textbooks

Similar questions

33. Let A be the n x n matrix with all 1's on the diagonal and all 0's above and below the diagonal. What is Ax, where x is a vector in R"?
Let (Ω, Pr) be a probability space, and let X and Y be two independent random variables that are positive and have non-zero variance. (a) Prove that X^2 and Y are independent. Note that by symmetry, it will also follow that Y^2 and X are independent. (b) Use the result from part (a) to show that the random variables W = X + Y and Z = XY are positively correlated (i.e. Cov(W, Z) > 0).
Let X1, X2, ... ,Xn form a random sample from U(0,0). Find minimal sufficient statistics.
Let U, V be two uniform independent random variables on [0, 2]. (a) Given U = 1, find the conditional expectation of 3U + 4V. (b) Given U = 1, find the conditional expectation of 3eU+V. (c) Given U = 1, find the conditional variance of 3U + 4V. (d) Given U + V = 3, find the conditional expectation of U - V and 3U + 4V. (Hint: consider the map g(u, v) = (u - v, u + v).)
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.
Is the following statements correct or incorrect: Suppose that a random vector Y' = (Y1, Y2, Y3) has multi-normal distribution with mean vector u and variance-covariance matrix £ given by and Σ 흑 0 1 respectively. CH), Then the distribution of Z = Y is N 1
Let (X₁, X₂) be a pair of standard exponential random variables with the countermonotonicity copula and let U be a standard uniform random variable. a) Find a stochastic representation of the form (X₁, X₂) = (f(U), g(U)) for functions f and g which shows how (X₁, X2) can be simulated. b) With the help of a), use software and numerical integration to calculate the minimal correlation for two standard exponential random variables.
For a GLM with canonical link function, explain how the likelihood equations imply that the residual vector e = (y – @) is orthogonal with C(X).
Let X and Y be independent and N(0, 1) distributed random variables. Let U = X and V = X/Y. Show that the random variable V is Cauchy distributed and find E(V ).
22 Let X and Y be jointly Gaussian random variables where oy= oy and p =-1. Find a transformation matrix such that new random variables Y, and Y, are statistically independent.
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 4.5 and a standard deviation of 1.9. Answer parts (a)-(d) below. (a) Find the probability that a randomly selected study participant's response was less than 4. The probability that a randomly selected study participant's response was less than 4 is (Round to four decimal places as needed.)
Consider the following two data vectors: A = [3,7,11]B=[3,2,1] Calculate the covariance matrix of these two vectors.