Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
Purchase Benefits
What is included with this book?
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 |
Table of Contents provided by Ingram. All Rights Reserved. |
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.