Methodology of Teaching Basic Knowledge in Probability Theory and Mathematical Statistics

Abstract

The article addresses the teaching of fundamental concepts in probability theory and mathematical statistics. Specifically, it discusses such concepts as experiment, realization of an experiment, outcome of an experiment as an elementary event, event, and probability space. An original auxiliary model called ‘Market’, proposed by N. Temirgaliyev, is introduced for studying the probability space of an experiment. Using the example of the standard experiment ‘coin tossing’ and the culturally rooted ‘asyk tossing’ (a traditional Kazakh game), auxiliary and probability spaces are constructed.

Additionally, the article presents a general scheme for constructing a probability space when the set of elementary events is finite. The practical significance of probability is also explored. A sequence of random numbers is generated, and based on it, a model of an experiment involving the tossing of a symmetrical and homogeneous die is developed. The frequency of a specific face of the die appearing is calculated for both a random sample and a series of experiments. In both cases, the Law of Large Numbers is confirmed, demonstrating the convergence of frequencies toward the event's probability as the number of trials increases.

Furthermore, the article discusses the methodology for presenting a general framework for constructing a probability space when the set of elementary events is finite, as well as methods for demonstrating the practical relevance of probability. A sequence of random numbers is again generated to model an experiment involving the tossing of a symmetrical and homogeneous die, and the frequency of a fixed face appearing is described for a random sample and for experimental series. In both instances, learners are given the opportunity to take their first scientific steps by observing the Law of Large Numbers in action, showing how the frequency of an event approaches its theoretical probability as the number of experiments increases.