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Unformatted text preview: i =1 ) i =1 P ( A i ) 4. Suppose P ( B ) > . Prove the following properties of conditional probability: (a) P ( A | B ) . (b) P ( | B ) = 1 (c) For A 1 , A 2 , . . . F with A i A j = for i 6 = j , P ( i =1 A i | B ) = i =1 P ( A i | B ) (d) AB = P ( A | B ) = 0 . (e) P ( B | B ) = 1 (f) A B P ( A | B ) P ( A ) (g) B A P ( A | B ) = 1 . 5. Prove the law of total probability. 1 6. Prove Bayes rule 7. Suppose A and B are independent events. Show that A and B c are also independent. 2...
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- Spring '08