Читать книгу Probability - Robert P. Dobrow - Страница 2

Table of Contents

Оглавление

COVER

TITLE PAGE

COPYRIGHT

DEDICATION

PREFACE

ACKNOWLEDGMENTS

ABOUT THE COMPANION WEBSITE

INTRODUCTION I.1 Walking the Web I.2 Benford's Law I.3 Searching the Genome I.4 Big Data I.5 From Application to Theory

1 FIRST PRINCIPLES 1.1 RANDOM EXPERIMENT, SAMPLE SPACE, EVENT 1.2 WHAT IS A PROBABILITY? 1.3 PROBABILITY FUNCTION 1.4 PROPERTIES OF PROBABILITIES 1.5 EQUALLY LIKELY OUTCOMES 1.6 COUNTING I 1.7 COUNTING II 1.8 PROBLEM-SOLVING STRATEGIES: COMPLEMENTS AND INCLUSION–EXCLUSION 1.9 A FIRST LOOK AT SIMULATION 1.10 SUMMARY EXERCISES

10  2 CONDITIONAL PROBABILITY AND INDEPENDENCE 2.1 CONDITIONAL PROBABILITY 2.2 NEW INFORMATION CHANGES THE SAMPLE SPACE 2.3 FINDING P(A AND B) 2.4 CONDITIONING AND THE LAW OF TOTAL PROBABILITY 2.5 BAYES FORMULA AND INVERTING A CONDITIONAL PROBABILITY 2.6 INDEPENDENCE AND DEPENDENCE 2.7 PRODUCT SPACES 2.8 SUMMARY EXERCISES

11  3 INTRODUCTION TO DISCRETE RANDOM VARIABLES 3.1 RANDOM VARIABLES 3.2 INDEPENDENT RANDOM VARIABLES 3.3 BERNOULLI SEQUENCES 3.4 BINOMIAL DISTRIBUTION 3.5 POISSON DISTRIBUTION 3.6 SUMMARY EXERCISES

12  4 EXPECTATION AND MORE WITH DISCRETE RANDOM VARIABLES 4.1 EXPECTATION 4.2 FUNCTIONS OF RANDOM VARIABLES 4.3 JOINT DISTRIBUTIONS 4.4 INDEPENDENT RANDOM VARIABLES 4.5 LINEARITY OF EXPECTATION 4.6 VARIANCE AND STANDARD DEVIATION 4.7 COVARIANCE AND CORRELATION 4.8 CONDITIONAL DISTRIBUTION 4.9 PROPERTIES OF COVARIANCE AND CORRELATION 4.10 EXPECTATION OF A FUNCTION OF A RANDOM VARIABLE 4.11 SUMMARY EXERCISES

13  5 MORE DISCRETE DISTRIBUTIONS AND THEIR RELATIONSHIPS 5.1 GEOMETRIC DISTRIBUTION 5.2 MOMENT-GENERATING FUNCTIONS 5.3 NEGATIVE BINOMIAL—UP FROM THE GEOMETRIC 5.4 HYPERGEOMETRIC—SAMPLING WITHOUT REPLACEMENT 5.5 FROM BINOMIAL TO MULTINOMIAL 5.6 BENFORD'S LAW 5.7 SUMMARY EXERCISES

14  6 CONTINUOUS PROBABILITY 6.1 PROBABILITY DENSITY FUNCTION 6.2 CUMULATIVE DISTRIBUTION FUNCTION 6.3 EXPECTATION AND VARIANCE 6.4 UNIFORM DISTRIBUTION 6.5 EXPONENTIAL DISTRIBUTION 6.6 JOINT DISTRIBUTIONS 6.7 INDEPENDENCE 6.8 COVARIANCE, CORRELATION 6.9 SUMMARY EXERCISES

15  7 CONTINUOUS DISTRIBUTIONS 7.1 NORMAL DISTRIBUTION 7.2 GAMMA DISTRIBUTION 7.3 POISSON PROCESS 7.4 BETA DISTRIBUTION 7.5 PARETO DISTRIBUTION 7.6 SUMMARY EXERCISES

16  8 DENSITIES OF FUNCTIONS OF RANDOM VARIABLES 8.1 DENSITIES VIA CDFS 8.2 MAXIMUMS, MINIMUMS, AND ORDER STATISTICS 8.3 CONVOLUTION 8.4 GEOMETRIC PROBABILITY 8.5 TRANSFORMATIONS OF TWO RANDOM VARIABLES 8.6 SUMMARY EXERCISES

17  9 CONDITIONAL DISTRIBUTION, EXPECTATION, AND VARIANCE INTRODUCTION 9.1 CONDITIONAL DISTRIBUTIONS 9.2 DISCRETE AND CONTINUOUS: MIXING IT UP 9.3 CONDITIONAL EXPECTATION 9.4 COMPUTING PROBABILITIES BY CONDITIONING 9.5 CONDITIONAL VARIANCE 9.6 BIVARIATE NORMAL DISTRIBUTION 9.7 SUMMARY EXERCISES

18  10 LIMITS 10.1 WEAK LAW OF LARGE NUMBERS 10.2 STRONG LAW OF LARGE NUMBERS 10.3 METHOD OF MOMENTS 10.4 MONTE CARLO INTEGRATION 10.5 CENTRAL LIMIT THEOREM 10.6 A PROOF OF THE CENTRAL LIMIT THEOREM 10.7 SUMMARY EXERCISES

19  11 BEYOND RANDOM WALKS AND MARKOV CHAINS 11.1 RANDOM WALKS ON GRAPHS 11.2 RANDOM WALKS ON WEIGHTED GRAPHS AND MARKOV CHAINS 11.3 FROM MARKOV CHAIN TO MARKOV CHAIN MONTE CARLO 11.4 SUMMARY EXERCISES

20  APPENDIX A: PROBABILITY DISTRIBUTIONS IN R

21  APPENDIX B: SUMMARY OF PROBABILITY DISTRIBUTIONS

22  APPENDIX C: MATHEMATICAL REMINDERS

23  APPENDIX D: WORKING WITH JOINT DISTRIBUTIONS

24  SOLUTIONS TO EXERCISES SOLUTIONS FOR CHAPTER 1 SOLUTIONS FOR CHAPTER 2 SOLUTIONS FOR CHAPTER 3 SOLUTIONS FOR CHAPTER 4 SOLUTIONS FOR CHAPTER 5 SOLUTIONS FOR CHAPTER 6 SOLUTIONS FOR CHAPTER 7 SOLUTIONS FOR CHAPTER 8 SOLUTIONS FOR CHAPTER 9 SOLUTIONS FOR CHAPTER 10 SOLUTIONS FOR CHAPTER 11

25  REFERENCES

26  INDEX

27  END USER LICENSE AGREEMENT

Probability

Подняться наверх