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
List of Tables
1 Chapter 1TABLE 1.1. Probability model for majors.TABLE 1.2. Events and sets.TABLE 1.3. Correspondence between subsets and binary lists.TABLE 1.4. Common values of binomial coefficients.TABLE 1.5. Voting outcomes for the ballot problem.
2 Chapter 2TABLE 2.1. Birthday probabilities.TABLE 2.2. Hypothetical 10,000 table.TABLE 2.3. Hypothetical 1000 table for color blindness.TABLE 2.4. Distribution of blood type in the United States.
3 Chapter 3TABLE 3.1. Probability distribution for the sum of two dice.TABLE 3.2. Distribution of number of children in US households.TABLE