To the question of trinomial functionals

Abstract

The article considers the properties of functionals from the trinomial distribution that appear in the tasks of statistical correction of the results of IDK-tests and knowledge quality estimation. For one of these functionals, variants of its definition at the "zero" point are proposed, and it is shown how one method of definition can be useful in calculating the mathematical expectation of such a functional, and another method of definition is useful in calculating the realizations of the functional within the task of knowledge quality estimation. The proposed indicator of the quality of knowledge assesses the student's confidence in the correctness of the answers during testing, and thus differs significantly from all existing assessment methods, which assess either the amount of knowledge, or rather relate to the assessment of abilities or skills, but not the quality of acquired knowledge. It is shown how the method of assessing the quality of knowledge is related to the policy of academic integrity in the educational environment. Assessment methods can both encourage the student to guess the correct answers and prevent them from violating the basics of academic integrity.