Midterm ReviewThe Big PictureThe Classical Statistical TrailDescriptive Statistics Power One-Lab OneConceptsSlide 6Exploratory Data AnalysisSlide 8Slide 9Box DiagramSlide 11Slide 12Power Three - Lab TwoOperations on eventsProbability statementsConditional ProbabilitySlide 17Slide 18Independence of two eventsSlide 20Power 4 – Lab TwoSlide 22The Probability of Getting k HeadsExpected Value of a discrete random variableVariance of a discrete random variableLab TwoSlide 27Hypothesis Testing: Rates & ProportionsRemaining TopicsMidterm Review Cont.Last TimeSlide 32Slide 33Slide 34Slide 35Slide 36InferenceConfidence IntervalsSlide 39Slide 40Hypothesis testsSlide 42Regression EstimatorsMinimize the sum of squared residualsSlide 45Inference in Regression Interval estimationEstimated Coefficients, Power 8Slide 48Inference in Regression Hypothesis testing11Midterm ReviewMidterm ReviewEcon 240AEcon 240A22The Big PictureThe Big PictureThe Classical Statistical TrailThe Classical Statistical TrailDescriptive StatisticsInferentialStatistics ProbabilityDiscrete RandomVariablesDiscrete Probability Distributions; MomentsBinomialApplicationRates &ProportionsPower 4-#444Descriptive StatisticsDescriptive StatisticsPower One-Lab OnePower One-Lab OneConceptsConceptscentral tendency: mode, median, meancentral tendency: mode, median, meandispersion: range, inter-quartile range, dispersion: range, inter-quartile range, standard deviation (variance)standard deviation (variance)Are central tendency and dispersion Are central tendency and dispersion enough descriptors?enough descriptors?55Concepts Concepts Normal DistributionNormal Distribution–Central tendency: mean or averageCentral tendency: mean or average–Dispersion: standard deviationDispersion: standard deviationNon-normal distributionsNon-normal distributionsDraw a HistogramDensity Function for the Standardized Normal Variate00.050.10.150.20.250.30.350.40.45-5 -4 -3 -2 -1 0 1 2 3 4 5Standard DeviationsDensityThe Classical Statistical TrailThe Classical Statistical TrailDescriptive StatisticsInferentialStatistics ProbabilityDiscrete RandomVariablesDiscrete Probability Distributions; MomentsBinomialApplicationRates &ProportionsPower 4-#4Classicall Modern77Exploratory Data AnalysisExploratory Data AnalysisStem and Leaf DiagramsStem and Leaf DiagramsBox and Whiskers PlotsBox and Whiskers Plots88Males: 140 145 160 190 155 165 150 190 195 138 160 155 153 145 170 175 175 170 180 135 170 157 130 185 190 155 170 155 215 150 145 155 155 150 155 150 180 160 135 160 130 155 150 148 155 150 140 180 190 145 150 164 140 142 136 123 155 Females: 140 120 130 138 121 125 116 145 150 112 125 130 120 130 131 120 118 125 135 125 118 122 115 102 115 150 110 116 108 95 125 133 110 150 108Weight Data991010Box DiagramBox DiagramFirst or lowest quartile;25% of observations belowUpper or highest quartile25% of observations abovemedian11113rd Quartile + 1.5* IQR = 156 + 46.5 = 202.5; 1st value below =195The Classical Statistical TrailThe Classical Statistical TrailDescriptive StatisticsInferentialStatistics ProbabilityDiscrete RandomVariablesDiscrete Probability Distributions; MomentsBinomialApplicationRates &ProportionsPower 4-#41313Power Three - Lab TwoPower Three - Lab TwoProbabilityProbability1414Operations on eventsOperations on eventsThe event A and the event B both The event A and the event B both occur:occur: Either the event A or the event B Either the event A or the event B occurs or both do:occurs or both do:The event A does not occur, i.e.not A:The event A does not occur, i.e.not A: )( BA )( BA A1515Probability statementsProbability statementsProbability of either event A or event BProbability of either event A or event B–if the events are mutually exclusive, thenif the events are mutually exclusive, then probability of event Bprobability of event B)()()()( BApBpApBAp )(1)( BpBp 0)( BAp 1616Conditional ProbabilityConditional ProbabilityExample: in rolling two dice, what is Example: in rolling two dice, what is the probability of getting a red one the probability of getting a red one given that you rolled a white one?given that you rolled a white one?–P(R1/W1) ?P(R1/W1) ?1717In rolling two dice, what is the probability of getting a red one giventhat you rolled a white one?1818Conditional ProbabilityConditional ProbabilityExample: in rolling two dice, what is Example: in rolling two dice, what is the probability of getting a red one the probability of getting a red one given that you rolled a white one?given that you rolled a white one?–P(R1/W1) ?P(R1/W1) ?)6/1/()36/1()1(/)11()1/1( WpWRpWRp 1919Independence of two eventsIndependence of two eventsp(A/B) = p(A)p(A/B) = p(A)–i.e. if event A is not conditional on event i.e. if event A is not conditional on event BB–thenthen )(*)( BpApBAp The Classical Statistical TrailThe Classical Statistical TrailDescriptive StatisticsInferentialStatistics ProbabilityDiscrete RandomVariablesDiscrete Probability Distributions; MomentsBinomialApplicationRates &ProportionsPower 4-#42121Power 4 – Lab TwoPower 4 – Lab Two2222HTHTpHT1-pp1 - ppHTHTHTHTp1-pp1-pThree flips of a coin; 8 elementary outcomes3 heads2 heads2 heads1 head2 heads1 head1 head0 heads2323The Probability of Getting k HeadsThe Probability of Getting k HeadsThe probability of getting k heads (along The probability of getting k heads (along a given branch) in n trials is: pa given branch) in n trials is: pk k *(1-*(1-p)p)n-kn-kThe number of branches with k heads in The number of branches with k heads in n trials is given by Cn trials is given by Cnn(k)(k)So the probability of k heads in n trials So the probability of k heads in n trials is is Prob(k) = CProb(k) = Cnn(k) p(k) pk k *(1-p)*(1-p)n-kn-kThis is the discrete binomial distribution This is the discrete binomial distribution where k can only take on discrete where k can only take on discrete values of 0, 1, …k values of 0, 1, …k2424Expected Value of a discrete Expected Value of a discrete random variablerandom variableE(x) =E(x) = the expected value of a discrete the expected value of a discrete random variable is the weighted random variable is the weighted average of the observations where average of the observations where the weight is the frequency of that the weight is the frequency of that observationobservationniixpix0)]([*)(2525Variance of a discrete random Variance of a discrete random
View Full Document
Unlocking...