Читать книгу Probability - Robert P. Dobrow - Страница 2
Table of Contents
Оглавление1 COVER
5 PREFACE
8 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
9 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
