Let X be a random variable taking three values: P(X = a₁) = P₁, P(X=a₂) = P2. P(X=03) = P3, where p₁ + P₂ + P3 = 1 and P₁, P2, P3 € (0, 1). Let A = {X = a₁} and G = {0, 0, A, Ac}. Prove that 1A. E (X³\G) = a²¹₁ + ª²P² + a³p3 ₁. P2 + P3

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