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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