Probability estimates for symmetric simple exclusion random walks
Probability in the alternative set theory
Probability inequalities for generalized -statistics.
Probability interpolating between free and boolean [Book]
Probability limit identification functions on separable metrizable spaces
Probability measure functors preserving infinite-dimensional spaces
Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables
In this article we continue formalizing probability and randomness started in [13], where we formalized some theorems concerning the probability and real-valued random variables. In this paper we formalize the variance of a random variable and prove Chebyshev's inequality. Next we formalize the product probability measure on the Cartesian product of discrete spaces. In the final part of this article we define the algebra of real-valued random variables.
Probability measures on compact semitopological semigroups
Probability measures with big kernels.
Probability on Finite Set and Real-Valued Random Variables
In the various branches of science, probability and randomness provide us with useful theoretical frameworks. The Formalized Mathematics has already published some articles concerning the probability: [23], [24], [25], and [30]. In order to apply those articles, we shall give some theorems concerning the probability and the real-valued random variables to prepare for further studies.
Probability structure preserving and absolute continuity
Probability that an element of a finite group has a square root
Let G be a finite group of even order. We give some bounds for the probability p(G) that a randomly chosen element in G has a square root. In particular, we prove that p(G) ≤ 1 - ⌊√|G|⌋/|G|. Moreover, we show that if the Sylow 2-subgroup of G is not a proper normal elementary abelian subgroup of G, then p(G) ≤ 1 - 1/√|G|. Both of these bounds are best possible upper bounds for p(G), depending only on the order of G.
Probability that n Random Points Are in Convex Position.
Probe on Network-Based Collaborative Maintenance Mode for After-Sales Equipment
Problém čtyř bodů
Článek se věnuje známé matematické úloze, která nese název problém čtyř bodů. Její řešení není jednoznačné, liší se podle volby pravděpodobnostního rozdělení bodů. Zde uvádíme řešení při volbě rovnoměrného rozdělení na množinách různých tvarů a porovnáváme jednotlivé výsledky.
Problem of uniqueness in the renewal process generated by the uniform distribution.
Problème de la glace pilée
Problème des martingales et équations différentielles stochastiques associées à un opérateur intégro-différentiel
Problèmes à frontière libre et arbres de mesures
Problèmes combinatoires posés par la physique statistique