Probability Models / Edition 1

Probability Models / Edition 1

by John Haigh, J. Haigh
     
 

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 analyze 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,… See more details below

Overview

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 analyze 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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Product Details

ISBN-13:
9781852334314
Publisher:
Springer London
Publication date:
09/24/2004
Series:
Springer Undergraduate Mathematics Series
Edition description:
1st ed. 2002. Corr. 2nd printing 2004
Pages:
256
Product dimensions:
6.84(w) x 9.28(h) x 0.64(d)

Related Subjects

Table of Contents

1Probability Spaces1
The Idea of Probability2
Laws of Probability3
Consequences5
Equally Likely Outcomes10
The Continuous Version16
Intellectual Honesty21
2Conditional Probability and Independence23
Conditional Probability23
Bayes' Theorem31
Independence36
The Borel-Cantelli Lemmas43
3Common Probability Distributions45
Common Discrete Probability Spaces45
Probability Generating Functions53
Common Continuous Probability Spaces54
Mixed Probability Spaces59
4Random Variables61
The Definition62
Discrete Random Variables63
Continuous Random Variables72
Jointly Distributed Random Variables75
Conditional Expectation88
5Sums of Random Variables93
Discrete Variables93
General Random Variables100
Records113
6Convergence and Limit Theorems117
Inequalities118
Convergence121
Limit Theorems129
7Stochastic Processes in Discrete Time139
Branching Processes140
Random Walks145
Markov Chains155
8Stochastic Processes in Continuous Time169
Markov Chains in Continuous Time169
Queues186
Renewal Theory200
Brownian Motion: The Wiener Process210
9Appendix: Common Distributions and Mathematical Facts223
Discrete Distributions223
Continuous Distributions224
Miscellaneous Mathematical Facts225
Bibliography227
Solutions229
Index253

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