Ebook: Probability Models

Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability via dice and cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. No specific knowledge of the subject is assumed, only a familiarity with the notions of calculus, and the summation of series. Where the full story would call for a deeper mathematical background, the difficulties are noted and appropriate references given. The main topics arise naturally, with definitions and theorems supported by fully worked examples and some 200 set exercises, all with solutions.

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Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability via dice and cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. No specific knowledge of the subject is assumed, only a familiarity with the notions of calculus, and the summation of series. Where the full story would call for a deeper mathematical background, the difficulties are noted and appropriate references given. The main topics arise naturally, with definitions and theorems supported by fully worked examples and some 200 set exercises, all with solutions.
Content:
Front Matter....Pages i-viii
Probability Spaces....Pages 1-22
Conditional Probability and Independence....Pages 23-44
Common Probability Distributions....Pages 45-60
Random Variables....Pages 61-91
Sums of Random Variables....Pages 93-116
Convergence and Limit Theorems....Pages 117-137
Stochastic Processes in Discrete Time....Pages 139-168
Stochastic Processes in Continuous Time....Pages 169-222
Appendix: Common Distributions and Mathematical Facts....Pages 223-226
Back Matter....Pages 227-256

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Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability via dice and cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. No specific knowledge of the subject is assumed, only a familiarity with the notions of calculus, and the summation of series. Where the full story would call for a deeper mathematical background, the difficulties are noted and appropriate references given. The main topics arise naturally, with definitions and theorems supported by fully worked examples and some 200 set exercises, all with solutions.
Content:
Front Matter....Pages i-viii
Probability Spaces....Pages 1-22
Conditional Probability and Independence....Pages 23-44
Common Probability Distributions....Pages 45-60
Random Variables....Pages 61-91
Sums of Random Variables....Pages 93-116
Convergence and Limit Theorems....Pages 117-137
Stochastic Processes in Discrete Time....Pages 139-168
Stochastic Processes in Continuous Time....Pages 169-222
Appendix: Common Distributions and Mathematical Facts....Pages 223-226
Back Matter....Pages 227-256
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