COMPLETE PRACTICAL TASKS ON RANDOM VARIABLES AND THEIR DISTRIBUTION FUNCTIONS

This paper presents a practice-oriented study of random variables and their distribution functions with an emphasis on applied problem solving. The work focuses on translating theoretical probability concepts into structured analytical tasks that develop statistical thinking and modeling skills. Discrete and continuous random variables are examined through practical exercises involving probability mass functions, probability density functions, cumulative distribution functions, and key numerical characteristics such as expectation, variance, and standard deviation. Special attention is given to interpreting distribution behavior, selecting appropriate models for real-world situations, and verifying results through logical consistency and mathematical justification. The study also demonstrates how distribution functions serve as a unifying framework for comparing different probabilistic models and supporting data-driven decision making. By combining theoretical rigor with systematic practical tasks, the paper aims to strengthen methodological understanding and improve the ability to apply probability tools in academic and applied contexts. The results highlight the pedagogical value of problem-based practice in mastering stochastic concepts and forming a solid foundation for further study in statistics, data analysis, and quantitative research.