lec1print

lec1print - Discrete probability Introduction to discrete...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

This note was uploaded on 01/17/2010 for the course STA 113 taught by Professor Staff during the Fall '08 term at Duke.

Page1 / 57

lec1print - Discrete probability Introduction to discrete...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online