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Unformatted text preview: Discrete probability Introduction to discrete probability Artin Armagan STA 113 Chapter 2 of Devore January 8, 2009 Artin Armagan Introduction to discrete probability Discrete probability Table of contents 1 Discrete probability Set theory Axioms Properties Combinatorics – counting Conditional probability Independence Artin Armagan Introduction to discrete probability Discrete probability Set theory Axioms Properties Combinatorics – counting Conditional probability Independence Probability Two types 1 Discrete – male or female, heads or tails, number of radioactive particles, how many buses go by, counts of nucleotides 2 Continuous – height of people, size of the head of a crab, length of time between volcanic eruptions, images (?), speech signals Artin Armagan Introduction to discrete probability Discrete probability Set theory Axioms Properties Combinatorics – counting Conditional probability Independence Discrete probability – counting Who are the best counters in the world ? Artin Armagan Introduction to discrete probability Discrete probability Set theory Axioms Properties Combinatorics – counting Conditional probability Independence Mathematics of counting and Kevin Bacon Combinatorics – http://en.wikipedia.org/wiki/Combinatorics. What does Paul Erd¨ os have to do with Kevin Bacon ? Artin Armagan Introduction to discrete probability Discrete probability Set theory Axioms Properties Combinatorics – counting Conditional probability Independence Sample space Definition A sample space S is the set of all possible outcomes of an experiment. Examples: 1 Experiment is flipping one coin – Sample space is { H , T } . 2 Experiment is flipping two coins – Sample space is { HH , TT , HT , TH } . 3 Experiment is flipping n coins – How many elements in the sample space ? Artin Armagan Introduction to discrete probability Discrete probability Set theory Axioms Properties Combinatorics – counting Conditional probability Independence Sample space Definition A sample space S is the set of all possible outcomes of an experiment. Examples: 5 Experiment is playing five rounds of Russian roulette – Sample space is { D , LD , LLD , LLLD , LLLD } . Why is this different than coin flipping. 6 Experiment is sequencing three nucleotides – Sample space is { AAA , CCC , GGG , TTT , AAC , AAT , AAG , ..., } . How big is this sample space ? (Hint: There are four nucleotides.) Artin Armagan Introduction to discrete probability Discrete probability Set theory Axioms Properties Combinatorics – counting Conditional probability Independence An event Definition A event is any collection of outcomes contained in the sample space, S . Examples: 1 Flipping one coin – Getting heads....
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 Fall '08
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 Probability, Probability theory, Conditional Probability Independence, Axioms Properties Combinatorics, Artin Armagan

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