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Basic Probability Theory for Biomedical EngineersRandom Variables

Basic Probability Theory for Biomedical Engineers: Random Variables [In many applications of probability theory, the experimental outcome space can be chosen to be a set of real numbers; for example, the outcome space for the toss of a single die can be S = {1, 2, 3, 4, 5, 6} just as well as the more abstract S = {ζ1, ζ2, • • • , ζ6}, where ζi represents the outcome that i dots appear on the top face of the die. In virtually all applications, a suitable mapping can be found from the abstract outcome space to the set of real numbers. Once this mapping is performed, all computations and analyses can be applied to the resulting real numbers instead of to the original abstract outcome space. This mapping is called a random variable, and enables us to develop a uniform collection of analytical tools which can be applied to any specific problem. Furthermore, this mapping enables us to deal with real numbers instead of abstract entities.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Basic Probability Theory for Biomedical EngineersRandom Variables

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2006
ISBN
978-3-031-00485-8
Pages
73 –123
DOI
10.1007/978-3-031-01613-4_2
Publisher site
See Chapter on Publisher Site

Abstract

[In many applications of probability theory, the experimental outcome space can be chosen to be a set of real numbers; for example, the outcome space for the toss of a single die can be S = {1, 2, 3, 4, 5, 6} just as well as the more abstract S = {ζ1, ζ2, • • • , ζ6}, where ζi represents the outcome that i dots appear on the top face of the die. In virtually all applications, a suitable mapping can be found from the abstract outcome space to the set of real numbers. Once this mapping is performed, all computations and analyses can be applied to the resulting real numbers instead of to the original abstract outcome space. This mapping is called a random variable, and enables us to develop a uniform collection of analytical tools which can be applied to any specific problem. Furthermore, this mapping enables us to deal with real numbers instead of abstract entities.]

Published: Jan 1, 2006

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