Introduction to Probability and Its Applications

by Scheaffer, Richard L.; Young, Linda

• ISBN13: 9780534386719
• ISBN10: 0534386717
• Edition: 3rd
• Format: Hardcover
• Copyright: 2009-08-21
• Publisher: Cengage Learning

Summary

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 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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