概率论

Preface

1Introduction

1.1EquallyLikelyOutcomes

1.2Interpretations

1.3Distributions

1.4ConditionalProbabilityandIndependence

1.5BayesRule

1.6SequencesofEvents

Summary

ReviewExercises

2RepeatedTrialsandSampling

2.1TheBinomialDistribution

2.2NormalApproximation:Method

2.3NormalApproximation:Derivation(Optional)

2.4PoissonApproximation

2.5RandomSampling

Summary

ReviewExercises

3RandomVariables

3.1Introduction

3.2Expectation

3.3StandardDeviationandNormalApproximation

3.4DiscreteDistributions

3.5ThePoissonDistribution

3.6Symmetry(Optional)

Summary

ReviewExercises

4ContinuousDistributions

4.1ProbabilityDensities

4.2ExponentialandGammaDistributions

4.3HazardRates(Optional)

4.4ChangeofVariable

4.5CumulativeDistributionFunctions

4.6OrderStatistics(Optional)

Summary

ReviewExercises

5ContinuousJointDistributions

5.1UniformDistributions

5.2Densities

5.3IndependentNormalVariables

5.4Operations(Optional)

Summary

ReviewExercises

6Dependence

6.1ConditionalDistributions:DiscreteCase

6.2ConditionalExpectation:DiscreteCase

6.3Conditioning:DensityCase

6.4CovarianceandCorrelation

6.5BivariateNormal

Summary

ReviewExercises

DistributionSummaries

Discrete

Continuous

Beta

Binomial

Exponential

Gamma

GeometricandNegativeBinomial

Hypergeometric

Normal

Poisson

Uniform

Examinations

SolutionstoExaminations

Appendices

1Counting

2Sums

3Calculus

4ExponentsandLogarithms

5NormalTable

BriefSolutionstoOdd-NumberedExercises

Index

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