Posterior Probability on Finite Set
In [14] we formalized probability and probability distribution on a finite sample space. In this article first we propose a formalization of the class of finite sample spaces whose element’s probability distributions are equivalent with each other. Next, we formalize the probability measure of the class of sample spaces we have formalized above. Finally, we formalize the sampling and posterior probability.
Pravděpodobnost a posteriori. [I.]
Pravděpodobnost a posteriori. [II.]
Principes d'invariance pour la probabilité d'un dilaté de l'enveloppe convexe d'un échantillon
Probabilidades en cadena en los espacios de Hilbert. Aplicaciones físicas.
Probability in the alternative set theory
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 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.
Product liftings and densities with lifting invariant and density invariant sections
Given two measure spaces equipped with liftings or densities (complete if liftings are considered) the existence of product liftings and densities with lifting invariant or density invariant sections is investigated. It is proved that if one of the marginal liftings is admissibly generated (a subclass of consistent liftings), then one can always find a product lifting which has the property that all sections determined by one of the marginal spaces are lifting invariant (Theorem 2.13). For a large...
Productos numerables de espacios normados probabilísticos.
Following the studies made by Alsina and Schweizer about countable products of probabilistic metric spaces, two kinds of products of probabilistic normed spaces are investigated.
Properties of a special class of doubly stochastic measures.