Final_Review_1

Final_Review_1 - Set Theory Operations and DeMorgans Laws...

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Set Theory Operations and DeMorgan’s Laws 1. Union (combination) 2. Intersection (common) 3. Complement (negation) A U B A ∩B A c 1. 2. 1. Containment (subset) A B A B Section 2.1 1
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Sample Spaces An experiment is a process whose outcome is uncertain (but it is known that it will be one of several possible outcomes). The sample space of an experiment is the set of all possible outcomes. An event is a collection (subset) of outcomes in the sample space. S E Experiment Events E 1 and E 2 are mutually exclusive (disjoint) if no outcome is in both E 1 and E 2 . E 1 E 2 = Φ E 1 E 2 E 1 and E 2 are DEPENDENT! Section 2.1 2
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Axioms and Properties of Probability Axioms: 1) P( S ) = 1 2) P( E ) 0 for every event E S 3) ℰ ℰ where i ⋂ ℰ j = Properties: 1) P( ) = 0, where is the “empty set” 2) 3) 4) Section 2.2 3
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Counting Techniques Equally likely events: S = E 1 ⋃ E 2 ⋃ ⋯ ⋃ E N ; P(E i )=1/N; P(A) = N(A)/N Product Rule for k -tuples: Counts the number of k -tuples you can create when there are n 1 choices for the first element, . .., n k choices for the
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This document was uploaded on 07/26/2011.

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Final_Review_1 - Set Theory Operations and DeMorgans Laws...

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