Probability Models

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Springer Science & Business Media, Jan 1, 2002 - Mathematics - 256 pages
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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.
  

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Contents

Probability Spaces
1
12 The Idea of Probability
2
13 Laws of Probability
3
14 Consequences
5
15 Equally Likely Outcomes
10
16 The Continuous Version
16
17 Intellectual Honesty
21
Conditional Probability and Independence
23
52 General Random Variables
100
53 Records
113
Convergence and Limit Theorems
117
61 Inequalities
118
62 Convergence
121
63 Limit Theorems
129
64 Summary
137
Stochastic Processes in Discrete Time
139

22 Bayes Theorem
31
23 Independence
36
24 The BorelCantelli Lemmas
43
Common Probability Distributions
45
32 Probability Generating Functions
53
33 Common Continuous Probability Spaces
54
34 Mixed Probability Spaces
59
Random Variables
61
41 The Definition
62
42 Discrete Random Variables
63
43 Continuous Random Variables
72
44 Jointly Distributed Random Variables
75
45 Conditional Expectation
88
Sums of Random Variables
93
71 Branching Processes
140
72 Random Walks
145
73 Markov Chains
155
Stochastic Processes in Continuous Time
169
82 Queues
186
83 Renewal Theory
200
The Wiener Process
210
Appendix Common Distributions and Mathematical Facts
223
92 Continuous Distributions
224
93 Miscellaneous Mathematical Facts
225
Bibliography
227
Solutions
229
Index
253
Copyright

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About the author (2002)

Mark Lewison has been a professional interior designer for over twenty years. He has worked for both residential and commercial clients throughout the United States. In addition to operating his interior design business, Mark is a full time faculty instructor at The Art Institute of California - Hollywood. Sherri Houtz holds a degree in English from Kutztown University in Pennsylvania. She grew up in Lancaster County, Pennsylvania with a love of travel, art, writing and design. Sherri has written a number of short stories, plays and screenplays. This is her first endeavor in non-fiction. Sherri currently resides in Los Angeles. John R. Haigh is a Southern Californian entrepreneur. He co-created the Mark On Call, Mark On Call HD and App Popular iOS apps that have been recommended in The Guardian, Good Housekeeping, Men's Health and MacWorld. "What Would You Do With This Room?" is his first collaboration in the literary field.

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