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This paper analyzes the treatment of the random variable and its applications on probability distributions in Chilean high school textbooks, from the Ontosemiotic Approach to Mathematical Knowledge and Instruction. Thus, a model is used for the analysis of mathematical objects in the Chilean textbooks and the Chilean school curriculum by means of content analysis. The results show a diversity of languages, concepts, propositions, procedures and arguments linked to the topics, although some of them are identified in the curriculum and excluded in books or inversely, showing a lack of coherence between the documents. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a critical and comparative analysis based on artistic proposals related to some diverse discursive strategies which have been developed during last decades in order to analyze and modify the spatial discourse. Space is understood as a technology to impose sex-gender fictions, and the works selected will be linked to various feminist, transfeminist, queer and post - colonial positionings. Through this text we present a systematization of different artistic approaches and we will reveal the spatial discourse as a mechanism to generate unequal experiences. The selected artistic proposals will show the capacity of space as capable of producing sex-gender differences, which are rooted in some binary and essentialist beliefs, and therefore excluding non standardized subjectivities beyond the heteronormative and cissexist binomial, as well as linking those exclusions to other intersectional discriminations. [ABSTRACT FROM AUTHOR]

The process of estimating a proportion that is associated with a sensitive question can yield responses that are not necessarily according to the reality. To reduce the probability o false response to this kind of sensitive questions some authors have proposed techniques of randomized response assuming a symmetric observation error. In this paper we present a generalization of the case where a symmetric error is assumed since this assumption could be unrealistic in practice. Under the assumption of an assymetric error the likelihood function is built. By doing this we intend that in practice the final user has an alternative method to reduce the probability of false response. Assuming informative a priori distributions an expresion for the posterior distribution is found. Since this posterior distribution does not have a closed mathematical expression, it is neccesary to use the Gibbs sampler to carry out the estimation process. This technique is illustrated using real data about drug consumptions that were collected by the Oficina de Bienestar from the Universidad Nacional de Colombia at Medellín. [ABSTRACT FROM AUTHOR]

One of the difficulties students from basic courses often show in learning probability and statistics at the university is understanding how the continuous normal probability distribution approximates the discrete binomial probability distribution. In this paper a didactic proposal is presented consisting in two algorithms, very easy to use, developed with software R which is completely free. These algorithms aim to introduce students in basic concepts of normal approximation to the binomial distribution by means of graphical representations and tables. They allow an active participation of student in the learning process. [ABSTRACT FROM AUTHOR]

Several approximations to the binomial distribution were compared in 1956 by Raft [9], including the normal, arcsine, normal Gram-Charlier, Camp-Paulson, Poisson, and Poisson Gram-Charlier approximations. The closeness of these approximations is judged by the maximal error which can arise in evaluating any sum of consecutive binomial terms. Borges [3] investigated a general class of approximations (which includes some of the above) and showed that a certain beta-transformation of a binomially distributed variable is the unique member of this class which is approximately normal with error 0(l/n). In 1963, Bol'shev [2] gave two new Poisson-type approximations. In this paper, some of Raft's tables are extended and tables for the error of these newer approximations are added. As a consequence of the numerical results obtained, the Poisson Gram-Charlier approximation is recommended for small values of p while the Camp-Paulson and Borges' approximations should generally be preferred for large p. [ABSTRACT FROM AUTHOR]