Lecture 5 b notes

# Lecture 5 b notes - Chapter 4 PROBABILITY THEORY Reference...

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Chapter 4 PROBABILITY THEORY Reference: Devore 7th Ed. Sections 2.1, 2.2. 4.1 Introduction 4.2 Basic model for probability Experiment, basic outcomes, sample space, events, probability function, axioms. 1. An “experiment” is an activity or process that is capable of generating two or more possible outcomes. (wide interpretation - could include a “survey”.) Example: Toss a dice – 6 possible basic outcomes of interest. Basic outcomes cannot be decomposed into anything simpler (that is useful). E.g. dice is odd is an outcome but not a basic outcome. 2. Sample space S = set of all basic outcomes. | S | = Number of outcomes in S , possibly infinity. Ex : Toss 1 dice S = { 1 , 2 , ..., 6 } | S | = 6 Toss 2 dice S = { (1 , 1) , (1 , 2) , ... (6 , 6) } | S | = 36 Project ball: distance S = (0 , 1000 feet) 3. Event is a subset of S . e.g. Dice experiment { 2,4,6 } Projectile (50, 60 feet) Can do usual manipulation with sets A, B events A B, A B, A c 1

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4. Probability function P () is a rule that assigns a number in [0,1] to each event. This number is called the probability of that event.
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• Spring '05
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• Game Theory, Probability theory, DeVore, basic outcomes

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