First Course in Probability, A (5th Edition)

✍ Scribed by Sheldon M. Ross

• Publisher: Prentice Hall College Div
• Year: 1997
• Tongue: English
• Leaves: 529
• Edition: 5
• Category: Library

✦ Synopsis

This market leader is written as an elementary introduction to the mathematical theory of probability for students in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus. A major thrust of the Fifth Edition has been to make the book more accessible to today's students. The exercise sets have been revised to include more simple, mechanical problems and a new section of Self-Test Problems with fully worked out solutions conclude each chapter. In addition, many new applications have been added to demonstrate the importance of probability in real situations. A software diskette, referenced in text and packaged with each copy of the book, provides an easy to use tool for students to derive probabilities for binomial, Poisson, and normal random variables, illustrate and explore the central limit theorem, work with the strong law of large numbers, and more.

✦ Table of Contents

Contents......Page 6
Preface......Page 12
1.1 Introduction......Page 16
1.2 The Basic Principle Of Counting......Page 17
1.3 Permutations......Page 18
1.4 Combinations......Page 20
1.5 Multinomial Coefficients......Page 25
1.6 On The Distribution Of Balls In Urns......Page 27
Summary......Page 30
Problems......Page 31
Theoretical Exercises......Page 34
Self-test Problems And Exercises......Page 38
2.2 Sample Space And Events......Page 40
2.3 Axioms Of Probability......Page 45
2.4 Some Simple Propositions......Page 47
2.5 Sample Spaces Having Equally Likely Outcomes......Page 51
2.6 Probability As A Continuous Set Function......Page 63
2.7 Probability As A Measure Of Belief......Page 67
Summary......Page 68
Problems......Page 69
Theoretical Exercises......Page 76
Self-test Problems And Exercises......Page 79
3.2 Conditional Probabilities......Page 82
3.3 Bayes' Formula......Page 87
3.4 Independent Events......Page 98
3.5 P(- | F) Is A Probability......Page 111
Summary......Page 118
Problems......Page 119
Theoretical Exercises......Page 133
Self-test Problems And Exercises......Page 138
4.1 Random Variables......Page 141
4.2 Distribution Functions......Page 146
4.3 Discrete Random Variables......Page 149
4.4 Expected Value......Page 151
4.5 Expectation Of A Function Of A Random Variable......Page 154
4.6 Variance......Page 157
4.7 The Bernoulli And Binomial Random Variables......Page 159
4.7.1 Properties Of Binomial Random Variables......Page 164
4.7.2 Computing The Binomial Distribution Function......Page 167
4.8 The Poisson Random Variable......Page 169
4.8.1 Computing The Poisson Distribution Function......Page 176
4.9.1 The Geometric Random Variable......Page 177
4.9.2 The Negative Binomial Random Variable......Page 179
4.9.3 The Hypergeometric Random Variable......Page 182
4.9.4 The Zeta (or Zipf) Distribution......Page 185
Summary......Page 186
Problems......Page 188
Theoretical Exercises......Page 199
Self-test Problems And Exercises......Page 204
14.2 Laplace Transforms......Page 207
5.2 Expectation And Variance Of Continuous Random Variables......Page 210
5.3 The Uniform Random Variable......Page 215
5.4 Normal Random Variables......Page 219
5.4.1 The Normal Approximation To The Binomial Distribution......Page 227
5.5 Exponential Random Variables......Page 230
5.5.1 Hazard Rate Functions......Page 235
5.6.1 The Gamma Distribution......Page 237
5.6.2 The Weibulldistribution......Page 239
5.6.3 The Cauchy Distribution......Page 240
5.6.4 The Beta Distribution......Page 241
5.7 The Distribution Of A Function Of A Random Variable......Page 242
Summary......Page 245
Problems......Page 247
Theoretical Exercises......Page 252
Self-test Problems And Exercises......Page 256
6.1 Joint Distribution Functions......Page 259
6.2 Independent Random Variables......Page 267
6.3 Sums Of Independent Random Variables......Page 279
6.4 Conditional Distributions: Discrete Case......Page 287
6.5 Conditional Distributions: Continuous Case......Page 288
6.6 Order Statistics......Page 291
6.7 Joint Probability Distribution Of Functions Of Random Variables......Page 295
6.8 Exchangeable Random Variables......Page 303
Summary......Page 306
Problems......Page 308
Theoretical Exercises......Page 315
Self-test Problem And Exercises......Page 320
7.1 Introduction......Page 324
7.2 Expectation Of Sums Of Random Variables......Page 325
7.3 Covariance, Variance Of Sums, And Correlations......Page 340
7.4.1 Definitions......Page 350
7.4.2 Computing Expectations By Conditioning......Page 352
7.4.3 Computing Probabilities By Conditioning......Page 359
7.4.4 Conditional Variance......Page 363
7.5 Conditional Expectation And Prediction......Page 365
7.6 Moment Generating Functions......Page 370
7.6.1 Joint Moment Generating Functions......Page 379
7.7.1 The Multivariate Normal Distribution......Page 380
7.7.2 The Joint Distribution Of The Sample Mean And Sample Variance......Page 381
7.8 General Definition Of Expectation......Page 383
Summary......Page 385
Problems......Page 387
Theoretical Exercises......Page 399
Self-test Problems And Exercises......Page 407
8.2 Chebyshev's Inequality And The Weak Law Of Large Numbers......Page 410
8.3 The Central Limit Theorem......Page 414
8.4 The Strong Law Of Large Numbers......Page 422
8.5 Other Inequalities......Page 427
8.6 Bounding The Error Probability When Approximating A Sum Of Independent Bernoulli Random Variables By A Poisson......Page 433
Problems......Page 436
Theoretical Exercises......Page 439
Self-test Problems And Exercises......Page 441
14.1 Differential Equations......Page 206
14.3 Difference Equations......Page 212
14.4 Z Transforms......Page 214
9.1 The Poisspn Process......Page 443
9.2 Markov Chains......Page 446
9.3 Surprise, Uncertainty, And Entropy......Page 451
Summary......Page 456
Theoretical Exercises And Problems......Page 463
References......Page 465
10.1 Introduction......Page 467
10.2.1 The Inverse Transformation Method......Page 470
10.2.2 The Rejection Method......Page 471
10.3 Simulating From Discrete Distributions......Page 477
10.4 Variance Reduction Techniques......Page 479
10.4.1 Use Of Antithetic Variables......Page 480
10.4.2 Variance Reduction By Conditioning......Page 481
Summary......Page 483
Problems......Page 484
References......Page 487
Appendix A Answers To Selected Problems......Page 488
Appendix B Solutions To Self-test Problems And Exercises......Page 492
Index......Page 528