Probability Distribution Functions

  • Luca Lista
Part of the Lecture Notes in Physics book series (LNP, volume 941)


The problem introduced in Sect. 1.6.1 with Bertrand’s paradox occurs when we try to decompose the range of possible values of a random variable x into equally probable elementary intervals and this is not always possible without ambiguity because of the continuous nature of the problem. In Sect. 1.6 we considered a continuous random variable x with possible values in an interval [x1, x2], and we saw that if x is uniformly distributed in [x1, x2], a transformed variable y = Y (x) is not in general uniformly distributed in [y1, y2] = [Y (x1), Y (x2)] (Y is taken as a monotonic function of x). This makes the choice of the continuous variable on which equally probable intervals are defined an arbitrary choice.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Luca Lista
    • 1
  1. 1.INFN Sezione di NapoliNapoliItaly

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