| Probability in the World Around Us | p. 1 |
| Why Study Probability? | |
| Deterministic and Probabilistic Models | p. 2 |
| Applications in Probability | p. 4 |
| A Brief Historical Note | p. 5 |
| A Look Ahead | p. 7 |
| Foundations of Probability | p. 8 |
| Randomness | p. 8 |
| Sample Space and Events | p. 13 |
| Definition of Probability | p. 22 |
| Counting Rules Useful in Probability | p. 31 |
| More Counting Rules Useful in Probability | p. 48 |
| Summary | p. 53 |
| Supplementary Exercises | p. 54 |
| Conditional Probability and Independence | p. 57 |
| Conditional Probability | p. 57 |
| Independence | p. 9 |
| Theorem of Total Probability and Bayes' Rule | p. 78 |
| Odds, Odds Rations, and Relative Risk | p. 83 |
| Summary | p. 88 |
| Supplementary Exercises | p. 88 |
| Discrete Probability Distributions | p. 93 |
| Random Variables and Their Probability Distributions | p. 93 |
| Expected Values of Random Variables | p. 104 |
| The Bernoulli Distribution | p. 121 |
| The Binomial Distribution | p. 122 |
| The Geometric Distribution | p. 137 |
| The Negative Binomial Distribution | p. 144 |
| The Poisson Distribution | p. 152 |
| The Hypergeometric Distribution | p. 162 |
| The Moment-Generating Function | p. 169 |
| The Probability-Generating Function | p. 172 |
| Markov Chains | p. 176 |
| Summary | p. 185 |
| Supplementary Exercises | p. 185 |
| Continuous Probability Distributions | p. 192 |
| Continuous Random Variables and Their Probability Distributions | p. 192 |
| Expected Values of Continuous Random Variables | p. 201 |
| The Uniform Distribution | p. 210 |
| The Exponential Distribution | p. 216 |
| The Gamma Distribution | p. 226 |
| The Normal Distribution | p. 233 |
| The Beta Distribution | p. 254 |
| The Weibull Distribution | p. 260 |
| Reliability | p. 267 |
| Moment-Generating Functions for Continuous Random Variables | p. 272 |
| Expectations of Discontinuous Functions and Mixed Probability Distributions | p. 276 |
| Summary | p. 281 |
| Supplementary Exercises | p. 281 |
| Multivariate Probability Distributions | p. 289 |
| Bivariate and Marginal Probability Distributions | p. 289 |
| Conditional Probability Distributions | p. 304 |
| Independent Random Variables | p. 309 |
| Expected Values of Functions of Random Variables | p. 313 |
| Conditional Expectations | p. 328 |
| The Multinomial Distribution | p. 335 |
| More on the Moment-Generating Function | p. 340 |
| Compounding and Its Applications | p. 342 |
| Summary | p. 344 |
| Supplementary Exercises | p. 344 |
| Functions of Random Variables | p. 351 |
| Introduction | p. 351 |
| Functions of Discrete Random Variables | p. 352 |
| Method of Distribution Functions | p. 354 |
| Method of Transformations in One Dimension | p. 363 |
| Method of Conditioning | p. 367 |
| Method of Moment-Generating Functions | p. 369 |
| Method of Transformation-Two Dimensions | p. 376 |
| Order Statistics | p. 381 |
| Probability-Generating Functions: Applications to Random Sums of Random Variables | p. 387 |
| Summary | p. 390 |
| Supplementary Exercises | p. 391 |
| Some Approximations to Probability Distributions: Limit Theorems | p. 395 |
| Introduction | p. 395 |
| Convergence in Probability | p. 395 |
| Convergence in Distributions | p. 399 |
| The Central Limit Theorem | p. 406 |
| Combination of Convergence in Probability and Convergence in Distributions | p. 419 |
| Summary | p. 420 |
| Supplementary Exercises | p. 421 |
| Extensions of Probability Theory | p. 422 |
| The Poisson Process | p. 422 |
| Birth and Death Processes: Biological Applications | p. 425 |
| Queues: Engineering Applications | p. 427 |
| Arrival Times for the Poisson Process | p. 428 |
| Infinite Server Queue | p. 430 |
| Renewal Theory: Reliability Applications | p. 431 |
| Summary | p. 435 |
| Appendix Tables | p. 438 |
| Answers to Selected Exercises | p. 449 |
| Index | p. 467 |
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