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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