Example_class_2_slides

Example_class_2_slides

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Unformatted text preview: to the sum of their individual lengths. Inclusion-Exclusion Principle n P (A1 ∪ · · · ∪ An ) = ∑ P (Ai ) − ∑ i =1 P (Ai1 ∩ Ai2 ) + · · · i1 <i2 +(−1)n−1 ∑ P (Ai1 ∩ Ai2 ∩ · · · ∩ Ain ) i1 <i2 <···<in n = ∑ (−1)j −1 j =1 where n can also be ∞. Chan Chi Ho, Chan Tsz Hin & Shi Yun ∑ P (Ai1 ∩ Ai2 ∩ · · · ∩ Aij ) i1 <i2 <···<ij Example class 2 Review Definition of conditional probability For any two events A and B , the conditional probability of A given the occurrence of B is written as P (A|B ) and is defined as P (A|B ) = P (A ∩ B ) P (B ) provided that P (B ) > 0. Multiplication theorem 1 For any two events A and B with P (B ) > 0, P (A ∩ B ) = P (B )P (A|B ). 2 For any three events A, B , C with P (B ∩ C ) > 0, P (A ∩ B ∩ C ) = P (C )P (B |C )P (A|B ∩ C ). Chan Chi Ho, Chan Tsz Hin & Shi Yun Example class 2 Review Independence 1 Two events A and B are called independent if and only if P (A ∩ B ) = P (A)P (B ). If P (A) > 0,then A and B are independent if P (B |A) = P (B ). 2 The events A1 , A2 , · · ·, Ak are (mu...
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This note was uploaded on 01/16/2012 for the course STAT 1301 taught by Professor Smslee during the Fall '08 term at HKU.

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