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5. In each step, explain clearly what property or axiom you are using. (a) Prove inclusion-exclusion, that P(AUB) P(A) +P(B)-P(AnB). (b) Prove the union bound, that P(AiUAz) < P(A) + P(A2). Under what conditions does the equality hold? (c) Prove that, for Ai and A2 disjoint, P(Ai UA2|B) P(AiB)P(A2|B) (d) A and B are independent events with nonzero probability. Prove whether or not A and B are independent.
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5. In each step, explain clearly what property or axiom you are using. (a) Prove "inclusion-exclusion,"...
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