Example_Class_2_handout

Example_Class_2_handout - THE UNIVERSITY OF HONG KONG...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 PROBABILITY AND STATISTICS I EXAMPLE CLASS 2 Review Set Theory and Mathematical Theory of Probability 1. De Morgan’s law n [ i =1 E i ! c = n \ i =1 E c i , n \ i =1 E i ! c = n [ i =1 E c i , where n can also be . 2. Language of Probability (a) Mutually exclusive A 1 ,A 2 , ··· ,A n are mutually exclusive if A i A j = φ for all i 6 = j . (b) Exhaustive A 1 ,A 2 , ··· ,A n are exhaustive if A 1 A 2 ∪ ··· ∪ A n = Ω . (c) Partition A 1 ,A 2 , ··· ,A n is called a partition if the events are mutually exclusive and exhaustive. (d) Complement The complement of event A is the collection of outcomes not in A, i.e. A c = Ω \ A 3. Kolmogorov’s Axiom (a) P ( A ) 0 for any event A (b) P (Ω) = 1 (c) For any sequence of mutually exclusive events A 1 ,A 2 ,... , P [ i =1 A i ! = X i =1 P ( A i ) (Countable additivity) Mnemonic trick: length of the union of disjoint segments is equal to the sum of their individual lengths. 4.
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Example_Class_2_handout - THE UNIVERSITY OF HONG KONG...

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