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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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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