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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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