Stat_ch3

# Stat_ch3 - Chapter 3 Probability Objectives Develop...

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Chapter 3 Probability

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2 Objectives Develop probability as a measure of uncertainty Introduce basic rules for finding probabilities Use probability as a measure of reliability for an inference
3 Events, Sample Spaces and Probability Experiment – process of observation that leads to a single outcome with no predictive certainty Sample point – most basic outcome of an experiment Sample Space – a listing of all sample points for an experiment Experiment – tossing 2 coins A Sample Point – HT Sample Space – S: {HH, HT, TH, TT} Sample point probability – relative frequency of the occurrence of the sample point

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4 Events, Sample Spaces and Probability Venn Diagram Sample Point Probabilities must lie between 0 and 1 The sum of all sample point probabilities must be one TH TT S Sample Space Name of Sample Space Sample Points
5 Events, Sample Spaces and Probability How to assign Sample Point Probabilities? Prior knowledge/assumption Multiple repetitions of an experiment Estimation based on survey Event – a specific collection of sample points Probability of an event – the sum of the probabilities of all sample points in the collection for the event

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6 Events, Sample Spaces and Probability How to assign Event Probabilities? Define experiment List sample points Assign probabilities to sample points Identify collection of sample points in Event Sum sample point probabilities
7 Events, Sample Spaces and Probability What is the probability of rolling an eight in a single toss of a pair of dice? Experiment is toss of pair of dice Probability of rolling an 8 = 1/36+1/36+1/36+1/36+1/36 = 5/36= .14 1,1 1,3 1,4 1,2 2,1 2,2 2,3 2,4 3,1 3,2 3,3 3,4 1,6 1,5 2,6 2,5 3,6 3,5 4,3 4,4 4,2 4,6 4,5 5,3 5,4 5,2 5,6 5,5 6,3 6,4 6,2 6,6 6,5 4,1 5,1 6,1 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36 1/36

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## This note was uploaded on 07/11/2008 for the course ECON V31.0018 taught by Professor Hall during the Summer '08 term at NYU.

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Stat_ch3 - Chapter 3 Probability Objectives Develop...

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