Introduction to Probability and Its Applications

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  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 8/21/2009
  • Publisher: Duxbury Press

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This text focuses on the utility of probability in solving real-world problems for students in a one-semester calculus-based probability course. Theory is developed to a practical degree and grounded in discussion of its practical uses in solving real-world problems. Numerous applications using up-to-date real data in engineering and the life, social, and physical sciences illustrate and motivate the many ways probability affects our lives. The text's accessible presentation carefully progresses from routine to more difficult problems to suit students of different backgrounds, and carefully explains how and where to apply methods. Students going on to more advanced courses in probability and statistics will gain a solid background in fundamental concepts and theory, while students who must apply probability to their courses engineering and the sciences will develop a working knowledge of the subject and appreciation of its practical power.

Table of Contents

Probability in the World Around Usp. 1
Why Study Probability?
Deterministic and Probabilistic Modelsp. 2
Applications in Probabilityp. 4
A Brief Historical Notep. 5
A Look Aheadp. 7
Foundations of Probabilityp. 8
Randomnessp. 8
Sample Space and Eventsp. 13
Definition of Probabilityp. 22
Counting Rules Useful in Probabilityp. 31
More Counting Rules Useful in Probabilityp. 48
Summaryp. 53
Supplementary Exercisesp. 54
Conditional Probability and Independencep. 57
Conditional Probabilityp. 57
Independencep. 9
Theorem of Total Probability and Bayes' Rulep. 78
Odds, Odds Rations, and Relative Riskp. 83
Summaryp. 88
Supplementary Exercisesp. 88
Discrete Probability Distributionsp. 93
Random Variables and Their Probability Distributionsp. 93
Expected Values of Random Variablesp. 104
The Bernoulli Distributionp. 121
The Binomial Distributionp. 122
The Geometric Distributionp. 137
The Negative Binomial Distributionp. 144
The Poisson Distributionp. 152
The Hypergeometric Distributionp. 162
The Moment-Generating Functionp. 169
The Probability-Generating Functionp. 172
Markov Chainsp. 176
Summaryp. 185
Supplementary Exercisesp. 185
Continuous Probability Distributionsp. 192
Continuous Random Variables and Their Probability Distributionsp. 192
Expected Values of Continuous Random Variablesp. 201
The Uniform Distributionp. 210
The Exponential Distributionp. 216
The Gamma Distributionp. 226
The Normal Distributionp. 233
The Beta Distributionp. 254
The Weibull Distributionp. 260
Reliabilityp. 267
Moment-Generating Functions for Continuous Random Variablesp. 272
Expectations of Discontinuous Functions and Mixed Probability Distributionsp. 276
Summaryp. 281
Supplementary Exercisesp. 281
Multivariate Probability Distributionsp. 289
Bivariate and Marginal Probability Distributionsp. 289
Conditional Probability Distributionsp. 304
Independent Random Variablesp. 309
Expected Values of Functions of Random Variablesp. 313
Conditional Expectationsp. 328
The Multinomial Distributionp. 335
More on the Moment-Generating Functionp. 340
Compounding and Its Applicationsp. 342
Summaryp. 344
Supplementary Exercisesp. 344
Functions of Random Variablesp. 351
Introductionp. 351
Functions of Discrete Random Variablesp. 352
Method of Distribution Functionsp. 354
Method of Transformations in One Dimensionp. 363
Method of Conditioningp. 367
Method of Moment-Generating Functionsp. 369
Method of Transformation-Two Dimensionsp. 376
Order Statisticsp. 381
Probability-Generating Functions: Applications to Random Sums of Random Variablesp. 387
Summaryp. 390
Supplementary Exercisesp. 391
Some Approximations to Probability Distributions: Limit Theoremsp. 395
Introductionp. 395
Convergence in Probabilityp. 395
Convergence in Distributionsp. 399
The Central Limit Theoremp. 406
Combination of Convergence in Probability and Convergence in Distributionsp. 419
Summaryp. 420
Supplementary Exercisesp. 421
Extensions of Probability Theoryp. 422
The Poisson Processp. 422
Birth and Death Processes: Biological Applicationsp. 425
Queues: Engineering Applicationsp. 427
Arrival Times for the Poisson Processp. 428
Infinite Server Queuep. 430
Renewal Theory: Reliability Applicationsp. 431
Summaryp. 435
Appendix Tablesp. 438
Answers to Selected Exercisesp. 449
Indexp. 467
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