Постановка проблеми в загальному вигляді. Сьогодні у світі здійснюється стрімка трансформація освіти від традиційної до цифрової, оскільки цифрова освіта − ключ до побудови іншої реальності, фундаменту нового життя суспільства. Оскільки сучасна освіта є найважливішим інстру-ментом ціннісного, соціально-економічного, політичного, культурного розвитку соціуму, вона повинна, безумовно, мати випереджальний характер, спираючись на прогнозні вимоги економіки й соціальної сфери країни в майбутній перспективі. Основним завданням національного рівня є фор

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The article analyzes some aspects of quality control and efficiency of electronic educational and methodological complexes of educational disciplines usage in the educational process. Analysis of the implementation of e-learning and of user work allows to build a model of student’s work, identify the disadvantages of both organizational and technological plan and take timely steps to eliminate them. The solution to this problem should include a comprehensive approach to ensure an objective result. Google Analytics tools, Moodle Learning Management System (LMS) tools, the teacher’s surveys to monitor the quality of e-learning in an institution proves its efficiency and allows to see the full advantages and disadvantages of ongoing e-learning in an institution, plan and implement further development and improving e-learning. The analysis of the effectiveness of e-courses usage should be carried out in a comprehensive manner, using the monitoring tools of the educational process adopted in the educational institution. Such as surveys for teachers and students, analysis of success, etc. The specifics of e-learning, the Moodle LMS tools and third-party services for collecting statistics and analyzing user activity in the LMS should be taken into account.

Introduction. Mathematical modeling of economic processes is necessary for the unambiguous formulation and solution of the problem. In the economic sphere this is the most important aspect of the activity of any enterprise, for which economic-mathematical modeling is the tool that allows to make adequate decisions. However, economic indicators that are factors of a model are usually random variables. An economic-mathematical model is proposed for calculating the probability distribution function of the result of economic activity on the basis of the known dependence of this result on factors influencing it and density of probability distribution of these factors. Methods. The formula was used to calculate the random variable probability distribution function, which is a function of other independent random variables. The method of estimation of basic numerical characteristics of the investigated functions of random variables is proposed: mathematical expectation that in the probabilistic sense is the average value of the result of functioning of the economic structure, as well as its variance. The upper bound of the variation of the effective feature is indicated. Results. The cases of linear and power functions of two independent variables are investigated. Different cases of two-dimensional domain of possible values of indicators, which are continuous random variables, are considered. The application of research results to production functions is considered. Examples of estimating the probability distribution function of a random variable are offered. Conclusions. The research results allow in the probabilistic sense to estimate the result of the economic structure activity on the basis of the probabilistic distributions of the values of the dependent variables. The prospect of further research is to apply indirect control over economic performance based on economic and mathematical modeling.

Digital transformation of education requires a higher educational institution to change its approach to the formation of professional competencies of future professionals. Development of digital competence, with Communication being one of its components, is an important aspect. The article substantiates the approaches of scholars to the interpretation of digital competence, namely its component Communication and Cooperation. The European framework and standards of digital competence of citizens and educators, which are an important tool in raising the level of digital competence of professionals, are analyzed and substantiated. The authors describe the DigComp framework of digital competence for citizens. The article describes the Digital Competence Wheel, on the basis of which in accordance with the DigComp framework, a questionnaire consisting of 24 descriptors, was developed to determine digital competence of future professionals. It has been proved that quality of the learning environment contributes to the formation of professional competencies, creates prerequisites for students' personal qualities development, provides training of a competitive specialist.