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3. Let X = (X1, X2) be an ordered pair that takes the points (-1,1), (0,0), and (1,1) with probabilities 1/4, 1/2, and 1/4. (1/4 if x1 =-1 and r2 = 1 1/2 ifxı = 0 and x2 = 0 1/4 ifr = 1 and r2 = 1 Px(r1, 12) = otherwise a. Show that X1 and X2 are not independent. b. Show that E[X1X2] = E[X¡] • E[X2].

3. Let X = (X1, X2) be an ordered pair that takes the points (-1,1), (0,0), and (1,1) with probabilities 1/4, 1/2, and 1/4. (1/4 if x1 =-1 and r2 = 1 1/2 ifxı = 0 and x2 = 0 1/4 ifr = 1 and r2 = 1 Px(r1, 12) = otherwise a. Show that X1 and X2 are not independent. b. Show that E[X1X2] = E[X¡] • E[X2].

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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3. Let X = (X1, X2) be an ordered pair that takes the points (-1, 1), (0,0), and (1, 1) with probabilities 1/4, 1/2, and 1/4. 1/4 if x1 = -1 and r2 = 1 1/2 ifr = 0 and x2 = 0 Px(x1, x2) = 1/4 ifrı = 1 and r2 = 1 otherwise a. Show that X1 and X2 are not independent. b. Show that E[X1X2] = E[X¡] · E[X»].
Transcribed Image Text:3. Let X = (X1, X2) be an ordered pair that takes the points (-1, 1), (0,0), and (1, 1) with probabilities 1/4, 1/2, and 1/4. 1/4 if x1 = -1 and r2 = 1 1/2 ifr = 0 and x2 = 0 Px(x1, x2) = 1/4 ifrı = 1 and r2 = 1 otherwise a. Show that X1 and X2 are not independent. b. Show that E[X1X2] = E[X¡] · E[X»].
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