Abstract
The problem introduced with Bertrand’s paradox occurs because the decomposition of the range of possible values of a random variable x into equally probable elementary cases is not possible without ambiguity. The concept of probability distribution can be generalized to the continuum case introducing the probability distribution function defined as follows.
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Notes
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This instant could also coincide with the occurrence of one of the considered events in order to apply the same derivation the time difference of two consecutive events.
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Lista, L. (2016). Probability Distribution Functions. In: Statistical Methods for Data Analysis in Particle Physics. Lecture Notes in Physics, vol 909. Springer, Cham. https://doi.org/10.1007/978-3-319-20176-4_2
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