Basic Notions of Probability Theory
This initial chapter covers background material that every serious student of applied probability should master. In no sense is the chapter meant as a substitute for a previous course in applied probability or for a future course in measure-theoretic probability. Our comments are merely meant as reminders and as a bridge. Many mathematical facts will be stated without proof. This is unsatisfactory, but it is even more unsatisfactory to deny students the most powerful tools in the probabilist’s toolkit. Quite apart from specific tools, the language and intellectual perspective of modern probability theory also furnish an intuitive setting for solving practical problems. Probability involves modes of thought that are unique within mathematics. As a brief illustration of the material reviewed, we derive properties of the multivariate normal distribution in the final section of this chapter. Later chapters will build on the facts and vocabulary mentioned here and provide more elaborate applications.
KeywordsRandom Vector Independent Random Variable Conditional Expectation Basic Notion Dominate Convergence Theorem
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