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Unformatted text preview: 2. For events E 1 , E 2 , ··· , E n , show that p ( E 1 ∩ E 2 ∩···∩ E n ) = P ( E 1 ) p ( E 2  E 1 ) P ( E 3  E 1 ∩ E 2 ) ··· P ( E n  E 1 ∩···∩ E n1 ) . 3. Prove Boole’s inequality: P ( ∪ n i =1 E i ) ≤ n X i =1 P ( E i ) . hint: First consider the simple case when n = 2. The idea is to try to partition ∪ n i =1 E i into disjoint set F i ’s, where F 1 = E 1 and F i = E i ∩ ( ∩ i1 j =1 E j ). 1...
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This note was uploaded on 01/02/2012 for the course MATH 2603 taught by Professor Han during the Spring '10 term at HKU.
 Spring '10
 Han
 Probability

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