Chapter 2 - Chapter 2. Probability 2.1 Sample Space and...

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Chapter 2. Probability 2.1 Sample Space and Events Random Experiment : The result of experiment is uncertain unpredictable one of the many outcomes e.g.) flipping a coin, tossing two dice, lifetime of a car Sample Space : The set of all possible outcomes of an experiment ( S , U ) Event : The subset of a sample space {: } A xx S =∈ Set theory S , A , B : set ' (union), (intersection), (complement) , A AB ∪∩ { } {0} φ =≠ = : mutually exclusive (disjoint) A BS = : mutually exhaustive
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2.2 Probability of an Event Probability Axiom : The probability of an event A is the sum of the weights of all sample points A. Therefore, 0( ) 1 , ( ) 0 , ( ) 1 PA P andPS φ ≤= = Furthermore, if 123 , , ,... AAA is a sequence of mutually exclusive events, then 1 2 3 () ( ) ( ) ( ) PA A A = +++ ∪∪∪ " " If an experiment can result in any one of N different equally likely outcomes, and if exactly n of these correspond to event A , then the probability of event A is n N = Properties 1. For any event A , ' () 1 ( ) =− 2. If A and B are mutually exclusive, then 0 PA B = 3. For any two event
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This note was uploaded on 10/02/2011 for the course STAT 3011 taught by Professor Wang,zhan during the Spring '09 term at Minnesota.

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Chapter 2 - Chapter 2. Probability 2.1 Sample Space and...

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