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settheory - Chapter 1 Probability and Distributions...

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Chapter 1: Probability and Distributions Introduction Set Theory The Probability Set Function Conditional Probability and Independence Random Variables—Discrete and Continuous Expection of a Random Variable
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I NTRODUCTION TO P ROBABILITY T HEORY Introduction Random Experiment: outcome can’t be predicted with certain but a collection of every possible outcome can be described before its performance. Ex.1: toss a coin Ex.2: Cast one red die and one white die Sample Space: collection of all possible outcome. Notation: C —sample space; c —one element; C —collection of the elements (Event). Ex.3: In Ex.2, let C be the collection of the pair for which the sum is 7 . What is C and what is the probability of event C .
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I NTRODUCTION TO P ROBABILITY T HEORY Set and Subset Set: a collection of the objects. C 1 = { x : 0 x 1 } ; C 2 = { ( x, y ) : 0 x + y < 3 } ; C 3 = { ( x, y, z ) : x 2 + y 2 + z 2 9 } . Element of the set or Point in the set: 1 4 C 1 ; (1 , 1) C 2 ; (0 , 0 , 0) C 3 .
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