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From the cases below, select those that offer enough information to be able to conclude that the random variables X and Y are independent. O a. X and Y are discrete random variables. Their joint cdf can be written as a product of the marginal cdf's, i.e. Fxy(x.y) Fx(x)Fy(9) holds for all x and y. O b. X and Y jointly follow a normal distribution and their covariance matrix has only non-negative entries. O. The conditional expectation and conditional variance of X given Y = y are both independent of y, i.e, neither E[ X|Y = y) nor Var( XY = y) depend on y. d. X and Y have zero covariance. e. The joint pdf f x.y of X and Y can be written in the form f x.y(x, y) (x)w(y) which holds for all values of x and y.

From the cases below, select those that offer enough information to be able to conclude that the random variables X and Y are independent. O a. X and Y are discrete random variables. Their joint cdf can be written as a product of the marginal cdf's, i.e. Fxy(x.y) Fx(x)Fy(9) holds for all x and y. O b. X and Y jointly follow a normal distribution and their covariance matrix has only non-negative entries. O. The conditional expectation and conditional variance of X given Y = y are both independent of y, i.e, neither E[ X|Y = y) nor Var( XY = y) depend on y. d. X and Y have zero covariance. e. The joint pdf f x.y of X and Y can be written in the form f x.y(x, y) (x)w(y) which holds for all values of x and y.

MATLAB: An Introduction with Applications
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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From the cases below, select those that offer enough information to be able to conclude that the random variables X and Y are independent. O a. X and Y are discrete random variables. Their joint cdf can be written as a product of the marginal cdfs, i.e. Fxx(x, y) Fx(x)Fy(y) holds for all x and y. b. X and Y jointly follow a normal distribution and their covariance matrix has only non-negative entries. c. The conditional expectation and conditional variance of X given Y = y are both independent of y, i.e, neither E[ X|Y = y] nor Var( X|Y = y) depend on y. d. X and Y have zero covariance. e. The joint pdf f x.y of X and Y can be written in the form f x.y(x, y) (x)w(y) which holds for all values of x and y.
Transcribed Image Text:From the cases below, select those that offer enough information to be able to conclude that the random variables X and Y are independent. O a. X and Y are discrete random variables. Their joint cdf can be written as a product of the marginal cdfs, i.e. Fxx(x, y) Fx(x)Fy(y) holds for all x and y. b. X and Y jointly follow a normal distribution and their covariance matrix has only non-negative entries. c. The conditional expectation and conditional variance of X given Y = y are both independent of y, i.e, neither E[ X|Y = y] nor Var( X|Y = y) depend on y. d. X and Y have zero covariance. e. The joint pdf f x.y of X and Y can be written in the form f x.y(x, y) (x)w(y) which holds for all values of x and y.
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