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Question: please i need clear writing if you choose to write...

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Please, I need clear writing if you choose to write by hand for a,b,c, and d.

thanks,

5. In each step, explain clearly what property or axiom you are using. (a) Prove inclusion-exclusion, that PAU B)-P(A)+P(B)-Pan B) (b) Prove the union bound that P(Ai UA2) P(Ai) P(A2). Under what conditions does the equality hold? (c) Prove that, for A and A2 disjoint, P(A UA2 B) P(A B)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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