Elements of applied probability : for engineering, mathematics and systems science / David McDonald.

Format:

Book

Author/Creator:

McDonald, David, 1947-

Contributor:

J. Fithian Tatem Memorial Fund.

Language:

English

Subjects (All):

Probabilities.

Physical Description:

xiii, 361 pages : illustrations ; 26 cm

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, [2004]

Summary:

This book has been designed for senior engineering, mathematics and systems science students. In addition, the author has used the optional, advanced sections as the basis for graduate courses in quality control and queueing. It is assumed that the students have taken a first course in probability but that some need a review. Discrete models are emphasized and examples have been chosen from the areas of quality control and telecommunications. The book provides correct, modern mathematical methods and at the same time conveys the excitement of real applications. Book jacket.

Contents:

1.1 Telecommunications and Quality Control 1

1.2 The Digital Network 1

1.3 Quality Control 6

1.5 A Probability Primer 17

1.6 A Random Sample 21

1.7 Joint Distributions 25

2 Modelling a Stochastic Process 31

2.1 The Probability Space 31

2.2 Random Variables 38

2.3 Expectation 44

2.4 Conditional Probabilities 48

2.5 Independence 52

2.6 General Random Variables 55

2.7 Independence of General Random Variables 57

2.8 The Kolmogorov Extension Theorem 59

3 Variables and Limit Theorems 71

3.1 Discrete Random Variables 71

3.2 Continuous Random Variables 76

3.3 Generating Functions 82

3.4 Law of Large Numbers 85

4 The Poisson Process 99

4.2 Bernoulli Point Processes 100

4.3 The Poisson Process 104

4.4 Applications of the Poisson Process 107

4.5 A Further Characterization 110

4.6 The Poisson Approximation 113

4.7 Nonhomogeneous Poisson Processes 119

5 Markov Chains 127

5.2 Steady-State Markov Chains 135

5.3 Convergence to Steady-State 140

5.4 Reversible Markov Chains 147

5.5 Hitting Probabilities 150

5.6 Proofs of Convergence to Steady State 161

5.7 Transience and Recurrence 165

5.8 Existence and the Strong Markov Property 169

5.9 The Watched Process 171

5.10 Foster's Criterion for Stability 175

6 Renewal Theory 183

6.2 Renewal Reward Processes 187

6.3 Stationary Renewal Processes 192

6.4 Convergence to Stationarity 203

6.5 Renewal with Nonlattice Variables 209

6.6 Homogeneous Coupling 210

6.7 The Bernoulli Part and Coupling 214

6.8 Proof of the Coupling Theorem 217

6.9 Regenerative Processes 221

7 Markov Processes 229

7.2 The Generator of a Markov Process 231

7.3 Queues and Time Reversal 242

7.4 Jackson Networks 250

7.5 Kelly or BCMP Networks 254

7.6 Approximation by a Markov Process 261

8 Markov Decision Theory 271

8.2 The Optimality Equation 276

8.3 Infinite Horizon Decision Problems 286

8.4 Continuous Time Decision Problems 295

8.5 Optimal Stopping 298

8.6 Quality Control - a Worst Case Analysis 308

9.1 Useful Results in Analysis 319

9.2 Integration and Expectation 319

9.3 Convexity 322

9.4 Norms and Fixed Points 324

9.5 Algebraic Results 327

9.8.1 Solutions to Selected Exercises in Chapter 1 334

9.8.2 Solutions to Selected Exercises in Chapter 2 336

9.8.3 Solutions to Selected Exercises in Chapter 3 338

9.8.4 Solutions to Selected Exercises in Chapter 4 342

9.8.5 Solutions to Selected Exercises in Chapter 5 346

9.8.6 Solutions to Selected Exercises in Chapter 6 349

9.8.7 Solutions to Selected Exercises in Chapter 7 352

9.8.8 Solutions to Selected Exercises in Chapter 8 354.

Notes:

Includes bibliographical references (pages 330-333) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the J. Fithian Tatem Memorial Fund.

ISBN:

9812387390

9812387404

OCLC:

55754402