Articoli correlati a Elementary Applications of Probability Theory
Sinossi
This book concerns applications of probability theory. It has been written in the hope that the techniques presented will be useful for problems in diverse areas. A majority of the examples come from the biological sciences but the concepts and techniques employed are not limited to that field. To illustrate, birth and death processes (Chapter 9) have applications to chemical reactions, and branching processes (Chapter 10)have applications in physics but neither of these specific applications is developed in the text. The book is based on an undergraduate course taught to students who have had one introductory course in probability and statistics. Hence it does not contain a lengthy introduction to probability and random variables, for which there are many excellent books. Prerequisites also include an elementary knowledge of calculus, including first-order differential equations, and linear algebra. The basic plan of the book is as follows. Chapter 1: a review of basic probability theory; Chapters 2-5: random variables and their applications; Chapter 6: sequences of random variables and concepts of convergence; Chapters 7-10: theory and properties of basic random processes. The outline is now given in more detail. Chapter 1 contains a brief review of some of the basic material which will be needed in later chapters; for example, the basic probability laws, conditional probability, change of variables, etc. It is intended that Chapter 1 be used as a reference rather than a basis for instruction. Students might be advised to study this chapter as the material is called upon.
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