IE3301-001 Fall 2013What is Probability?What is Statistics?Data CollectionMethods of Statistical AnalysisChapter 1 Descriptive StatisticsChapter 1 cont’d...Chapter 2 Probability TheoryChapter 2 cont’d...Slide 10Homework AssignmentsIE3301-001 Fall 2013IE3301-001 Fall 2013SyllabusSyllabusOverview of Chapters 1 & 2Overview of Chapters 1 & 2Homework AssignmentsHomework AssignmentsWhat is Probability?What is Probability?A method for representing random A method for representing random eventsevents or or outcomesoutcomesExamplesExamples•Flip a coinFlip a coin•Roll a six-sided dieRoll a six-sided die•# of people in line when you enter the post office# of people in line when you enter the post office•The favorite color of the person sitting in the first seat The favorite color of the person sitting in the first seat of the first rowof the first rowWhat is Statistics?What is Statistics?Techniques for Techniques for collectingcollecting and and analyzinganalyzing datadata, so as , so as to to make decisionsmake decisions about the about the populationpopulation that that generated the datagenerated the data•Note: “data” is plural and “datum” is singularNote: “data” is plural and “datum” is singularExample populationsExample populations•SAT scoresSAT scores for freshman entering UTA in 2002 for freshman entering UTA in 2002•SalariesSalaries of professors at UTA of professors at UTA•PricesPrices of a gallon of milk in Arlington today of a gallon of milk in Arlington today•DiametersDiameters of pipes from a manufacturing process of pipes from a manufacturing processData CollectionData CollectionGoal: Collect a set of data from a populationGoal: Collect a set of data from a populationTypes of DataTypes of Data•Experimental data: designed and controlledExperimental data: designed and controlled•Observational data: uncontrolledObservational data: uncontrolledSamplingSampling•Simple Random Sampling: Every value in the Simple Random Sampling: Every value in the population is equally likely to be selectedpopulation is equally likely to be selected•Target population = Sampled populationTarget population = Sampled populationMethods of Statistical AnalysisMethods of Statistical AnalysisDescriptive StatisticsDescriptive Statistics•Methods for summarizing raw dataMethods for summarizing raw dataInferential StatisticsInferential Statistics•Methods for Methods for statistical inferencestatistical inference•Estimation of unknown Estimation of unknown parametersparameters (e.g., the central value)(e.g., the central value)•Decisions based on specific Decisions based on specific hypotheseshypotheses (e.g., Is the average pipe diameter > 10 cm?)(e.g., Is the average pipe diameter > 10 cm?)Chapter 1 Descriptive Statistics Chapter 1 Descriptive Statistics Measures of LocationMeasures of Location•MeanMean•MedianMedian•Mode (Ch. 8)Mode (Ch. 8)•Percentiles & Quartiles (Ch. 8)Percentiles & Quartiles (Ch. 8)Measures of VariabilityMeasures of Variability•Sample RangeSample Range•Variance and Standard DeviationVariance and Standard Deviation•Coefficient of Variation (Ch. 8)Coefficient of Variation (Ch. 8)Chapter 1 Chapter 1 cont’d...cont’d...Tabular SummariesTabular Summaries•Stem and Leaf PlotStem and Leaf Plot•Count or FrequencyCount or Frequency•Relative and Cumulative FrequencyRelative and Cumulative FrequencyGraphical MethodsGraphical Methods•Histogram (Bar Chart)Histogram (Bar Chart)•Empirical Cumulative Distribution (Bar Chart)Empirical Cumulative Distribution (Bar Chart)•Ogive (Line Chart)Ogive (Line Chart)•Boxplot (Ch. 8)Boxplot (Ch. 8)Chapter 2 Probability TheoryChapter 2 Probability TheorySample Spaces and EventsSample Spaces and Events•Random Experiments Random Experiments (with/without sampling replacement)(with/without sampling replacement)•Sample SpaceSample Space•EventsEvents•Review set operationsReview set operations•Tree DiagramsTree Diagrams•CombinationsCombinationsChapter 2 Chapter 2 cont’d...cont’d...Probability InterpretationsProbability Interpretations•Degree of Belief / Relative Frequency Degree of Belief / Relative Frequency •Equally Likely OutcomesEqually Likely Outcomes•PP((EE) = Probability of an Event ) = Probability of an Event EESet NotationSet Notation•EE11EE22 = Union of events = Union of events EE11 and and EE22•EE11EE22 = Intersection of events = Intersection of events EE11 and and EE22•E'E' = Complement of event = Complement of event EEProbability AxiomsProbability AxiomsChapter 2 Chapter 2 cont’d...cont’d...Addition RulesAddition RulesConditional ProbabilityConditional Probability•PP((BB||AA) = probability of event ) = probability of event BB given event given event AAIndependent Events Independent Events Multiplicative RuleMultiplicative RuleTotal Probability RuleTotal Probability RuleBayes’ RuleBayes’ RuleHomework AssignmentsHomework AssignmentsHW #1 due Wednesday, September 4HW #1 due Wednesday, September 4•pg 30: 1.13, 1.17, 1.19bc, 1.20bcdpg 30: 1.13, 1.17, 1.19bc, 1.20bcd•pg 42: 2.3, 2.11pg 42: 2.3, 2.11HW #2 due Wednesday, September 11HW #2 due Wednesday, September 11•pg 51: 2.23, 2.25, 2.47pg 51: 2.23, 2.25, 2.47•pg 59: 2.49, 2.53, 2.63pg 59: 2.49, 2.53, 2.63•pg 69: 2.73, 2.83, 2.89pg 69: 2.73, 2.83, 2.89•pg 76: 2.95, 2.97, 2.99pg 76: 2.95, 2.97,