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Description IV: Further Topics in Probability

  • John D. Robson
  • Colin J. Dodds
  • Donald B. Macvean
  • Vincent R. Paling
Part of the International Centre for Mechanical Sciences book series (CISM, volume 115)

Abstract

Given a random variable having a probability density function p(x), we introduce the Fourier transform Φ(u): \(\Phi \left( u \right) = \int\limits_{ - \infty }^\infty {{e^{ - ixu}}p\left( x \right)} \cdot dx\), and conversely We write the transform and the inverse in the more usual form with the factor 2π, since the interpretation of u as a frequency is meaningless here; some authors, however, interchange the signs of the exponent in these formulae.

Keywords

Characteristic Function Probability Density Function Random Function Thetical Function Usual Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1971

Authors and Affiliations

  • John D. Robson
    • 1
    • 2
  • Colin J. Dodds
    • 1
  • Donald B. Macvean
    • 1
  • Vincent R. Paling
    • 1
  1. 1.University of GlasgowUK
  2. 2.UdineItaly

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