Let A and B be arbitrary random events. a) Prove that if A and B are statistically independent, then A and B are statistically independent. (Hint: start from the definition of statistical independence and total probability) b) Suppose you are now informed that: P(A) = 0.2, Determine: (i) (ii) (111) P(An B) = 0.3, P(An B) = 0.15 P(A/B) P(An B) Are A and B statistically independent? Show your reasoning for full credit.