Browsing Faculties by Author "Kachapova, F"
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A measure of monotonicity of two random variables
Kachapova, F; Kachapov, I (Science Publications, 2012)Problem statement: When analyzing random variables it was useful to measure the degree of their monotone dependence or compare pairs of random variables with respect to their monotonicity. Existing coefficients measure ... 
Applying change of variable to calculus problems
Kachapova, F; Kachapov, I (Taylor & Francis, 2011)The paper describes the technique of introducing a new variable in some calculus problems that helps students to master the skills of integration and evaluating limits. This technique is algorithmic and easy to apply; it ... 
Finding the envelope and efficient frontier of financial assets
Kachapova, F; Kachapov, I (Science Publications, 2012)Problem statement: One of the problems considered in financial mathematics is finding portfolios of given financial assets that minimize risk for targeted returns. The set of such portfolios is called the envelope of the ... 
Formalizing Probability Concepts in a Type Theory
Kachapova, F (Science Publications, 2018)In this paper we formalize some fundamental concepts of probability theory such as the axiomatic definition of probability space, random variables and their characteristics, in the Calculus of Inductive Constructions, which ... 
Measuring monotony in twodimensional samples
Kachapova, F; Kachapov, I (Taylor & Francis, 2010)The paper introduces a monotony coefficient as a new measure of the monotone dependence in a twodimensional sample. Some properties of this measure are derived. In particular, it is shown that the absolute value of the ... 
Monotonicity criteria
Kachapova, F; Kachapov, I (World Academy of Science, Engineering and Technology (WASET), 2013)Monotonicity is an important type of dependence of random variables. The paper reviews the definitions of comonotonicity and countermonotonicity, their existing criteria and introduces a new criterion for each of the two ... 
Orthogonal projection in teaching regression and financial mathematics
Kachapova, F; Kachapov, I (ASA Publications, 2010)Two improvements in teaching linear regression are suggested. The first is to include the population regression model at the beginning of the topic. The second is to use a geometric approach: to interpret the regression ... 
Paradoxes and counterexamples in teaching and learning of probability at university
Klymchuk, S; Kachapova, F (Taylor & Francis, 2011)This article is devoted to practical aspects of teaching and learning of probability at university. It presents the difficulties and attitudes of firstyear university science and engineering students towards using paradoxes ... 
Percentage problems in bridging courses
Kachapova, F; Kachapov, I (Taylor and Francis, 2012)Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging ... 
Representing Markov chains with transition diagrams
Kachapova, F (Science Publications, 2013)Stochastic processes have many useful applications and are taught in several university programmes. Students often encounter difficulties in learning stochastic processes and Markov chains, in particular. In this article ... 
Students’ misconceptions about random variables
Kachapova, F; Kachapov, I (Taylor & Francis, 2011)This article describes some misconceptions about random variables and related counterexamples, and makes suggestions about teaching initial topics on random variables in general form instead of doing it separately for ...