class03_3 - 1.017/1.010 Class 3 Probability Conceptual...

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1.017/1.010 Class 3 Probability Conceptual framework Probability theory provides a conceptual framework for analyzing uncertain outcomes of experiments Definitions An experiment is defined by: 1. A set of experimental outcomes 2. A collection of events constructed from these outcomes 3. A rule which assigns probabilities to the events Definition of outcomes is problem/context dependent. Sample space S is set of all possible experimental outcomes An event is a set of outcomes. An elementary event is a single outcome. Probability P ( A ) of an event A is a number assigned to the event that meets the following requirements (probability axioms): 1. P ( A ) 0 2. P ( S ) = 1 3. P ( A 1 + A 2 +... + A N ) = P ( A 1 ) + P ( A 2 ) + ... + P ( A N ) For A 1 + A 2 = A 1 A U 2 A 1 A 2 = A 1 I A 2 = 0 ( A 1 , A 2 are mutually exclusive events) Note A 1 + A 2 and A 1 A 2 are distinct events with their own probabilities P ( A ) is intended to convey the likelihood that A occurs, on a scale from 0 to 1 Probability properties (follow from axioms) 1. P ( A 1 + A 2 ) = P ( A 1 ) + P ( A 2 ) - P ( A 1 A 2 ) for A 1 A 2
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