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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 (Ω  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
 Stites,M
 Conditional Probability, Probability, Probability theory, #, Utah State University

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