Lecture1 - Introduction to Probability and Set Theory Notes...

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Introduction to Probability and Set Theory Introduction Set Theory Probability 1.1 Lecture 1 Introduction to Probability and Set Theory Text: A Course in Probability by Weiss 1 . 2 2 . 3 STAT 225 Introduction to Probability Models January 13, 2014 Whitney Huang Purdue University Introduction to Probability and Set Theory Introduction Set Theory Probability 1.2 Agenda 1 Introduction 2 Set Theory 3 Probability Notes Notes
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Introduction to Probability and Set Theory Introduction Set Theory Probability 1.3 Motivation Uncertainty/Randomness in our life Will it snow tomorrow? Can LeBron James and the Miami Heat win a third NBA title this year? If I flip a coin 100 times, what are the chances I get 50 heads and 50 tails? We often want to assess how likely of such event occurs Probability is the right tool Introduction to Probability and Set Theory Introduction Set Theory Probability 1.4 Definitions Probability theory is based on the paradigm of a random experiment , i.e. an action whose outcome cannot be predicted beforehand. Element: a single item (outcome), typically denoted by ω Set: a collection of elements Sample space: the set of all possible outcomes for a random experiment and is denoted by Ω Subset: a set itself which every element is contained in a large set. Notes Notes
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Introduction to Probability and Set Theory Introduction Set Theory Probability 1.5 Sample Space, Set, Subset * * * * ω (Proper) Subset Set Sample space Ω Introduction to Probability and Set Theory Introduction Set Theory
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