Chapter 3. Probability

Chapter 3. Probability - 3 3.1 Probability Notation and set...

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§ 3 Probability § 3.1 Notation and set operations 3.1.1 Recall that Ω is a sample space. Consider events A,B Ω. Notation Meaning Examples A B either A or B { 1 , 2 , 3 } ∪ { 1 , 3 , 5 } = { 1 , 2 , 3 , 5 } { x 1 } ∪ { x < 0 } = { x 1 } A B both A and B { 1 , 2 , 3 } ∩ { 1 , 3 , 5 } = { 1 , 3 } { x 1 } ∩ { x < 0 } = { x < 0 } A \ B A but not B { 1 , 2 , 3 } \ { 1 , 3 , 5 } = { 2 } { x 1 } \ { x < 0 } = { 0 x 1 } A B A implies B { 1 , 2 } ⊂ { 0 , 1 , 2 , 3 } { x < 0 } ⊂ { x 1 } 3.1.2 For any event A , “not A ” is denoted by A c (= Ω \ A ), the complement of A in Ω. Example. If Ω = { 0 , 1 , 2 , 3 ,... } , { 1 , 2 , 3 } c = { 0 , 4 , 5 ,... } . 3.1.3 Denote an “impossible event” by , the empty set . Note: Ω can be regarded as a “certain” event. 3.1.4 Some useful set operations : Let A,B,A 1 ,A 2 ,... be any events in Ω. ( A 1 A 2 ) A 3 = A 1 ( A 2 A 3 ) ( A 1 A 2 ) A 3 = A 1 ( A 2 A 3 ) ( A 1 A 2 ∩ ··· ) B
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Chapter 3. Probability - 3 3.1 Probability Notation and set...

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