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Book Categories |
1 | Probability Spaces | 1 |
The Idea of Probability | 2 | |
Laws of Probability | 3 | |
Consequences | 5 | |
Equally Likely Outcomes | 10 | |
The Continuous Version | 16 | |
Intellectual Honesty | 21 | |
2 | Conditional Probability and Independence | 23 |
Conditional Probability | 23 | |
Bayes' Theorem | 31 | |
Independence | 36 | |
The Borel-Cantelli Lemmas | 43 | |
3 | Common Probability Distributions | 45 |
Common Discrete Probability Spaces | 45 | |
Probability Generating Functions | 53 | |
Common Continuous Probability Spaces | 54 | |
Mixed Probability Spaces | 59 | |
4 | Random Variables | 61 |
The Definition | 62 | |
Discrete Random Variables | 63 | |
Continuous Random Variables | 72 | |
Jointly Distributed Random Variables | 75 | |
Conditional Expectation | 88 | |
5 | Sums of Random Variables | 93 |
Discrete Variables | 93 | |
General Random Variables | 100 | |
Records | 113 | |
6 | Convergence and Limit Theorems | 117 |
Inequalities | 118 | |
Convergence | 121 | |
Limit Theorems | 129 | |
7 | Stochastic Processes in Discrete Time | 139 |
Branching Processes | 140 | |
Random Walks | 145 | |
Markov Chains | 155 | |
8 | Stochastic Processes in Continuous Time | 169 |
Markov Chains in Continuous Time | 169 | |
Queues | 186 | |
Renewal Theory | 200 | |
Brownian Motion: The Wiener Process | 210 | |
9 | Appendix: Common Distributions and Mathematical Facts | 223 |
Discrete Distributions | 223 | |
Continuous Distributions | 224 | |
Miscellaneous Mathematical Facts | 225 | |
Bibliography | 227 | |
Solutions | 229 | |
Index | 253 |
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