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Table of Contents
1 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