Models for Probability and Statistical Inference: Theory and Applications (Wiley Series in Probability and Statistics)

467 Pages·2007·6.76 MB·English

by  James H. Stapleton

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Models for Probability and
Statistical Inference
Theory and Applications
JAMESH.STAPLETON
MichiganStateUniversity
DepartmentofStatisticsandProbability
EastLansing,Michigan
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Models for Probability and
Statistical Inference
i
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ii
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Models for Probability and
Statistical Inference
Theory and Applications
JAMESH.STAPLETON
MichiganStateUniversity
DepartmentofStatisticsandProbability
EastLansing,Michigan
iii
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Stapleton,JamesH.,1931–
Modelsforprobabilityandstatisticalinference:theoryandapplications/JamesH.Stapleton.
p.cm.
ISBN978-0-470-07372-8(cloth)
1.Probabilities—Mathematicalmodels. 2.Probabilities—Industrialapplications. I.Title.
QA273.S74152008
519.2—dc22 2007013726
PrintedintheUnitedStatesofAmerica
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ToAlicia,whohasmademyfirsthomesopleasant
foralmost44years.
ToMichiganStateUniversityanditsDepartmentofStatistics
andProbability,mysecondhomeforalmost49years,
towhichIwillalwaysbegrateful.
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Contents
Preface xi
1. DiscreteProbabilityModels 1
1.1. Introduction, 1
1.2. SampleSpaces,Events,andProbabilityMeasures, 2
1.3. ConditionalProbabilityandIndependence, 15
1.4. RandomVariables, 27
1.5. Expectation, 37
1.6. TheVariance, 47
1.7. CovarianceandCorrelation, 55
2. SpecialDiscreteDistributions 62
2.1. Introduction, 62
2.2. TheBinomialDistribution, 62
2.3. TheHypergeometricDistribution, 65
2.4. TheGeometricandNegativeBinomialDistributions, 68
2.5. ThePoissonDistribution, 72
3. ContinuousRandomVariables 80
3.1. Introduction, 80
3.2. ContinuousRandomVariables, 80
3.3. ExpectedValuesandVariancesforContinuousRandomVariables, 88
3.4. TransformationsofRandomVariables, 93
3.5. JointDensities, 97
3.6. DistributionsofFunctionsofContinuousRandomVariables, 104
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