Axiomatic approach to probability theory
In this book, the authors combine a rigorous and yet easy axiomatic approach to probability theory with numerous examples of environmental applications. The book is written as a treatise on basic probabilistic concepts and methods.
This approach can provide students and practicing environmentalists with a convenient, practical guide to the theoretical issues, and simultaneously present specific conceptual approaches in the development of useful environmental applications.
The authors have chosen the direct way of presenting the main probabilistic concepts, using examples of corresponding environmental issues as illustrations and sources of probability problems. This book can be regarded as a necessary introductory guide to probability theory and its logic for the students and professionals who will have to ameliorate and/or manage environmental issues.
Contents:
Experiments and events; Space of elementary events; Probability of random events; Conditional probability and stochasitic indepdence: multistage probabilistic evaluation and forecasting; Bernoulli distribution and sequences of independent trials; Random variables and distribution functions; Numerical characteristics of random variables: mathematical expectation, variance, and moments of higher order; Numerical characteristics of random variables: quantiles; Probability distributions: discrete case; Probability distributions: continuous case; Limit theorems of the probability theory; and, Probabilistic decision making. Appendices include: Principles of set theory; Methods of counting; Statistical comparison of an original data set with it's subset in oil spill studies; and, Standard normal distribution function.
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