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
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
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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
Transcribed Image Text: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
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