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NetMathOnlineMathCourses,UniversityofIllinois CourseSyllabusforMATH461(IntroductiontoProbabilityTheory) Coursedescription:Introductiontomathematicalprobability;includesthecalculusof probability,combinatorialanalysis,randomvariables,expectation,distribution functions,moment‐generatingfunctions,andcentrallimittheorem. Probability and Statistics Authors: Bill Davis and Jerry Uhl ©2006-2010 Publisher: Making Math, a division of O’Reilly Media Credit:3hours. Prerequisite:MATH241orequivalent. Required Material:Please Visit - https://netmath.illinois.edu/mathable Syllabus: Prob.01 MonteCarloSimulations EstimatingprobabilitiesandmeasurementsbyMonteCarlosimulation. Prob.02 DataAnalysis Frequency,cumulativedistributionfunctionsandhistogramsfordatasetsofnumbers. Expectedvalueandvariancefordatasetsandfunctionsofdatasets. Prob.03 Probabilities Probabilitiesofunionsandintesectionsofdatasets.Conditionalprobabilityand independence.Serieswiringversusparallelwiring.Drugtesting.Birthday problem.Probabilityofwinningatcraps.Gambler'sruin. Prob.04 MoreDataAnalysis Markov'sinequality,Chebyshev'sinequalitiesandstandarddeviation.Lawoflarge numbers.RandomWalks,Outliers. Prob.05 NormalandExponential Normaldistributionandthebellcurve.Exponentialdistributionandtheexponentialcurve. Recognizingdatasetsthatareapproximatelynormallyorexponentiallydistributed.The memorylesspropertyoftheexponentialdistribution.MonteCarlogenerationofnormally orexponentiallydistributeddatasets.Experimentswithsampleaveragesandthenormal distribution. Prob.06 RandomVariables Continuousversusdiscreterandomvariables.Approximationofcontinuousrandom variablesbydiscreterandomvariables.Probabilitydensityfunctionsandcumulative distributionfunctions.Brandnamecontinuousdistributions:uniform,normal,exponential, Weibull,chi‐square,gammaandbeta.Sampleusesofeach.MonteCarlogenerationofdata setsfollowingaspecifieddistribution. Prob.07 JointDistributions Jointdistributions:DiscreteandContinuous.Independence,conditionalprobabilityand conditionalexpectations.Corellation. Prob.08 GeneratingfunctionsandtheCentralLimitTheorem Centrallimittheorem.Generatingfunctions.Specialattentiontosumsofindependent normalandexponentialrandomvariables. Prob.09 Counting Permutations,combinations,Bernoulli,Binomial,andPoissondistributions. Approximationsbynormaldistributions. Prob.10 Statistics Samplingforthemeanandvariance.Acceptancetesting.
