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.]
Probabilidades en cadena en los espacios de Hilbert. Aplicaciones físicas.
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.
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.