확률과 통계 2판 솔루션 (저자 Bertsekas , Tsitsiklis , 2nd ed Introduction to Probability)

Introduction to Probability 2nd Edition Problem Solutions
(last updated: 7/31/08)

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Dimitri P. Bertsekas and John N. Tsitsiklis
Massachusetts Institute of Technology

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CHAPTER 1

Solution to Problem 1.1. We have A 〓 {2, 4, 6}, so A ∪ B 〓 {2, 4, 5, 6}, and (A ∪ B)c 〓 {1, 3}. On the other hand, Ac ∩ B c 〓 {1, 3, 5} ∩ {1, 2, 3} 〓 {1, 3}. Similarly, we have A ∩ B 〓 {4, 6}, and (A ∩ B)c 〓 {1, 2, 3, 5}. On the other hand, Ac ∪ B c 〓 {1, 3, 5} ∪ {1, 2, 3} 〓 {1, 2, 3, 5}. Solution to Problem 1.2. (a) By using a Venn diagram it can be seen that for any sets S and T , we have S 〓 (S ∩ T ) ∪ (S ∩ T c ). (Alternatively, argue that any x must belong to either T or to T c , so x belongs to S if and only if it belongs to S ∩ T or to S ∩ T c .) Apply this equality with S 〓 Ac and T 〓 B, to obtain the ?rst relation Ac 〓 (Ac ∩ B) ∪ (Ac ∩ B c ). Interc…