Displaying similar documents to “Random split of the interval [0,1]”

On random split of the segment

Milena Bieniek, Dominik Szynal (2005)

Applicationes Mathematicae

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We consider a partition of the interval [0,1] by two partition procedures. In the first a chosen piece of [0,1] is split into halves, in the second it is split by uniformly distributed points. Initially, the interval [0,1] is divided either into halves or by a uniformly distributed random variable. Next a piece to be split is chosen either with probability equal to its length or each piece is chosen with equal probability, and then the chosen piece is split by one of the above procedures....

An extended problem to Bertrand's paradox

Mostafa K. Ardakani, Shaun S. Wulff (2014)

Discussiones Mathematicae Probability and Statistics

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Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by...

Survival probability approach to the relaxation of a macroscopic system in the defect-diffusion framework

Paulina Hetman (2004)

Applicationes Mathematicae

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The main objective of this paper is to present a new probabilistic model underlying the universal relaxation laws observed in many fields of science where we associate the survival probability of the system's state with the defect-diffusion framework. Our approach is based on the notion of the continuous-time random walk. To derive the properties of the survival probability of a system we explore the limit theorems concerning either the summation or the extremes: maxima and minima. The...

Probability on Finite and Discrete Set and Uniform Distribution

Hiroyuki Okazaki (2009)

Formalized Mathematics

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A pseudorandom number generator plays an important role in practice in computer science. For example: computer simulations, cryptology, and so on. A pseudorandom number generator is an algorithm to generate a sequence of numbers that is indistinguishable from the true random number sequence. In this article, we shall formalize the "Uniform Distribution" that is the idealized set of true random number sequences. The basic idea of our formalization is due to [15].