Let X be a random variable taking three values:P(X = a₁) = P₁,P(X=a₂) = P2₁P(X=03) = P3,where p₁ + P2 + P3 = 1 and P₁, P2, P3 € (0, 1). Let A = {X = a₁} and G = {2, 0, A, Ac}. ProvethatE (X³|G) = a1₁ +0²0² +0²P³ 14².P2 + P3

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Answered: Let X be a random variable taking three…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let X be a random variable taking three values: P(X = a₁) = P₁, P(X=a₂) = P2₁ P(X=03) = P3, where p₁ + P2 + P3 = 1 and P₁, P2, P3 € (0, 1). Let A = {X = a₁} and G = {2, 0, A, Ac}. Prove that E (X³|G) = a1₁ + 0²0² +0²P³ 14². P2 + P3