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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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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 PY(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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References

  1. L. I. Goldfischer: J. Opt. Soc. Am. 55, 247 (1965)

    Article  ADS  Google Scholar 

  2. J. C. Dainty: Opt. Acta 17, 761 (1970)

    Article  ADS  Google Scholar 

  3. D. Korff: Opt. Commun. 5, 188 (1972)

    Article  Google Scholar 

  4. J. C. Dainty (ed.): Laser Speckle and Related Phenomena, 2nd ed., Topics in Applied Physics, Vol. 9 (Springer, Berlin, Heidelberg, New York 1982)

    Google Scholar 

  5. J. W. Goodman: Proc. IEEE 53, 1688 (1965)

    Article  Google Scholar 

  6. K. Miyamoto: “Wave Optics and Geometrical Optics in Optical Design,” in Progress in Optics, Vol. 1, ed. by E. Wolf (North-Holland, Amsterdam 1961)

    Google Scholar 

  7. J. J. Burke: J. Opt. Soc. Am. 60, 1262 (1970)

    Article  ADS  Google Scholar 

  8. W. Feller: An Introduction to Probability Theory and Its Applications, Vol. 2 (Wiley, New York 1966) p. 50

    Google Scholar 

  9. J. W. Strohbehn: In Laser Beam Propagation in the Atmosphere, ed. J. W. Strohbehn, Topics in Applied Physics, Vol. 25 (Springer, Berlin, Heidelberg, New York 1978)

    Google Scholar 

  10. R. L. Phillips and L. C. Andrews: J. Opt. Soc. Am. 72, 864 (1982)

    Article  ADS  Google Scholar 

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Authors and Affiliations

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

    Professor B. Roy Frieden Ph. D.

Authors
  1. Professor B. Roy Frieden Ph. D.
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© 1991 Springer-Verlag Berlin Heidelberg

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Frieden, B.R. (1991). Functions of Random Variables. In: Probability, Statistical Optics, and Data Testing. Springer Series in Information Sciences, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97289-8_5

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  • DOI: https://doi.org/10.1007/978-3-642-97289-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53310-8

  • Online ISBN: 978-3-642-97289-8

  • eBook Packages: Springer Book Archive

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