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.
A Review of Basic Probability Theory
Some Applications of the Hypergeometric and Poisson Distributions
Simulation and Random Numbers
Convergence of Sequences of Random Variables: The Central Limit Theorem and the Laws of Large Numbers
Simple Random Walks
Population Genetics and Markov Chains
Population Growth I: Birth and Death Processes
Population Growth II: Branching Processes
Stochastic Processes and an Introduction to Stochastic Differential Equations
Diffusion Processes, Stochastic Differential Equations and Applications
Appendix: Table of Critical Values of the X2-Distribution