details are in the image 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 = 11/2 ifr = 0 and x2 = 0Px(x1, x2) =1/4 ifrı = 1 and r2 = 1otherwisea. Show that X1 and X2 are not independent.b. Show that E[X1X2] = E[X¡] · E[X»].

Answered: Image /qna-images/answer/88209b8c-276a-488f-b48c-a05c863307e6.jpg

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].

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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details are in the image

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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