Probability - Robert P. Dobrow

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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

      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

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