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Functions of Random Variables

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Probability, Statistical Optics, and Data Testing

Part of the book series: Springer Series in Information Sciences ((SSINF,volume 10))

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  • The book was inadvertently published with missing figures in several chapters of this book. This has been added in the affected chapters.

Abstract

Consider the notion of a “square-law” detector: If x is an input to the detector, then y = x 2 is its output or detected value. Consider next the case where x is a random variable with probability law p X(x). Then output y is also random. If so, what is its probability law p Y(y)? Certainly this should depend in some way upon p X(x), since x and y are closely related by the transformation y = x 2. The general question of how to find the law p Y(y) for a transformed or output RV is the subject of this chapter.

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Authors and Affiliations

  1. Optical Research Center, University of Arizona, Tucson, AZ, 85721, USA

    Professor B. Roy Frieden

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  1. Professor B. Roy Frieden
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© 2001 Springer-Verlag Berlin Heidelberg

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Frieden, B.R. (2001). Functions of Random Variables. In: Probability, Statistical Optics, and Data Testing. Springer Series in Information Sciences, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56699-8_5

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  • DOI: https://doi.org/10.1007/978-3-642-56699-8_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41708-8

  • Online ISBN: 978-3-642-56699-8

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