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Task of the day (a) If Z=aX+bY and r is the correlation coefficient between X and Y, show that o2=a²o²+ b²oy² + 2abrox Oy. (b) Show that the correlation coefficient r between two random variables X and Y is given by r = (0x² + 0²-0²x-y) / 20xOy, where ox, oy and ox-y are the standard deviations of X, Y and X - Y respectively.

Task of the day (a) If Z=aX+bY and r is the correlation coefficient between X and Y, show that o2=a²o²+ b²oy² + 2abrox Oy. (b) Show that the correlation coefficient r between two random variables X and Y is given by r = (0x² + 0²-0²x-y) / 20xOy, where ox, oy and ox-y are the standard deviations of X, Y and X - Y respectively.

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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Task of the day (a) If Z=aX+ bY and r is the correlation coefficient between X and Y, show that o²=a²oy² + b²oy² + 2abrox Oy. (b) Show that the correlation coefficient r between two random variables X and Y is given by r = (0x² + 0²-0²x-y) / 20x Oy, where ox, oy and Ox-y are the standard deviations of X, Y and X - Y respectively.
Transcribed Image Text:Task of the day (a) If Z=aX+ bY and r is the correlation coefficient between X and Y, show that o²=a²oy² + b²oy² + 2abrox Oy. (b) Show that the correlation coefficient r between two random variables X and Y is given by r = (0x² + 0²-0²x-y) / 20x Oy, where ox, oy and Ox-y are the standard deviations of X, Y and X - Y respectively.
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