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1、AnIntroductiontoStatisticalInferenceandDataAnalysisMichaelW.Trosset1April3,20011DepartmentofMathematics,CollegeofWilliam&Mary,P.O.Box8795,Williamsburg,VA23187-8795.Contents1MathematicalPreliminaries51.1Sets................................51.2Counting..................
2、...........91.3Functions.............................141.4Limits...............................151.5Exercises.............................162Probability172.1InterpretationsofProbability..................172.2AxiomsofProbability......................182.3FiniteSampleSp
3、aces.......................262.4ConditionalProbability.....................322.5RandomVariables........................432.6Exercises.............................513DiscreteRandomVariables553.1BasicConcepts..........................553.2Examples.......................
4、......563.3Expectation............................613.4BinomialDistributions......................723.5Exercises.............................774ContinuousRandomVariables814.1AMotivatingExample......................814.2BasicConcepts..........................854.3Eleme
5、ntaryExamples......................884.4NormalDistributions.......................934.5NormalSamplingDistributions.................9712CONTENTS4.6Exercises.............................1025QuantifyingPopulationAttributes1055.1Symmetry.............................1055.2
6、Quantiles.............................1075.2.1TheMedianofaPopulation...............1115.2.2TheInterquartileRangeofaPopulation........1125.3TheMethodofLeastSquares..................1125.3.1TheMeanofaPopulation................1135.3.2TheStandardDeviationofaPopulation...
7、.....1145.4Exercises.............................1156SumsandAveragesofRandomVariables1176.1TheWeakLawofLargeNumbers................1186.2TheCentralLimitTheorem...................1206.3Exercises.............................1277Data1297.1ThePlug-InPrinciple.............
8、.........1307.2Plug-InEstimatesofMeanandVariance............1327.3Plug-InEstimatesofQuantiles.................1347.3.1BoxPlo
