Elementary Applications of Probability Theory: with an Introduction to Stochastic Differential EquationsMaterial type: TextSeries: Texts in statistical sciencePublication details: London ; New York : Chapman and Hall, 1995Edition: 2ndDescription: xv, 292 pages : illustrationsISBN: 9780412576201; 0412576201 Subject(s): ProbabilitiesDDC classification: 519.201
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1. review of basic probability theory --
2. Geometric probability --
3. Some applications of the hypergeometric and Poisson distributions --
4. Reliability theory --
5. Simulation and random numbers --
6. Convergence of sequences of random variables: the central limit theorem and the laws of large numbers --
7. Simple random walks --
8. Population genetics and Markov chains --
9. Population growth I: birth and death processes --
10. Population growth II: branching processes --
11. Stochastic processes and an introduction to stochastic differential equations --
12. Diffusion processes, stochastic differential equations and applications --
Appendix: Table of critical values of the [actual symbol not reproducible]
This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering.
The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth.
This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.