INTEGRATING CONTEXTUAL EDUCATION INTO TEACHING PROBABILITY THEORY AND MATHEMATICAL STATISTICS FOR ENGINEERING MAJORS.

KIRISH: this article analyzes the problems arising in teaching "Probability Theory and Mathematical Statistics" at technical universities and the role of contextual education technology in overcoming them. The issues of students' transition from deterministic to probabilistic-statistical thinking are considered, and the advantages of contextual education are demonstrated using practical examples from the field of communication. MAQSAD: tadqiqotning asosiy maqsadi texnika oliy o‘quv yurtlarida "Ehtimollar nazariyasi va matematik statistika" fanini o‘qitishda kontekstli ta’lim texnologiyasining o‘rnini asoslash hamda amaliy, kasbga yo‘naltirilgan masalalar yordamida ushbu yondashuvning samaradorligini ko‘rsatib berishdan iborat. MATERIALLAR VA METODLAR: tadqiqot jarayonida oliy ta’limda matematik tayyorgarlik va kontekstli ta’lim nazariyasiga oid ilmiy-pedagogik manbalar tahlil qilindi. Metodologik asos sifatida matematik modellashtirish usullari, ehtimollar nazariyasining klassik apparati (Bayes formulasi, Erlang qonuniyatlari), tizimli tahlil hamda zamonaviy dasturiy paketlar (Statistica, Statgraphics) imkoniyatlaridan foydalanildi. MUHOKAMA VA NATIJALAR: maqolada aloqa tarmoqlarida axborot uzatish va radioto‘lqinlar orqali ma’lumotlar oqimini tahlil qilishga oid amaliy misollar ko‘rib chiqildi. Bayes formulasi yordamida signallarni uzatish va qabul qilishdagi ehtimolliklarni hisoblash hamda umumlashtirilgan Erlang qonuni asosida ma’lumotlarni uzatish vaqtini modellashtirish orqali kontekstli ta’limning talabalarda mantiqiy va kasbiy fikrlashni rivojlantirishdagi afzalliklari ko‘rsatildi. XULOSA: ehtimollar nazariyasi va matematik statistikani abstrak nazariy usulda emas, balki bo‘lajak kasbiy faoliyat kontekstida o‘qitish talabalarning mustaqil ta’lim olish va tahlil qilish ko‘nikmalarini oshiradi. Dasturiy paketlardan foydalangan holda amaliy va laboratoriya mashg‘ulotlarini tashkil etish bo‘lajak muhandislarning raqobatbardoshligini ta’minlashda yuqori samaradorlik ko‘rsatadi.

INTRODUCTION: ushbu maqolada texnika oliy o‘quv yurtlarida "Ehtimollar nazariyasi va matematik statistika" fanini o‘qitishda yuzaga keladigan muammolar va ularni bartaraf etishda kontekstli ta’lim texnologiyasining roli tahlil qilingan. Maqolada talabalarda deterministik fikrlashdan ehtimoliy-statistik fikrlashga o‘tish muammolari ko‘rib chiqilgan va aloqa sohasiga oid amaliy misollar yordamida kontekstli ta’limning afzalliklari ko‘rsatib berilgan. AIM: the main objective of this study is to analyze the pedagogical effectiveness of contextual education in teaching probability theory and mathematical statistics at technical universities, demonstrating its benefits through real-world engineering problems. MATERIALS AND METHODS: the research employs an analytical review of pedagogical literature on higher mathematics education and contextual learning frameworks. The methodological approach combines theoretical probability tools (such as Bayes' theorem and Erlang distribution models) with practical data analysis methods, incorporating the application of specialized statistical software packages (e.g., Statistica, Statgraphics) in laboratory training. DISCUSSION AND RESULTS: the paper presents practical contextual problems drawn from the telecommunications field, including calculating signal sequence transmission probabilities via Bayes' formula and evaluating data transmission durations using generalized Erlang laws. The results demonstrate that aligningmathematical content with the student's professional domain bridges the gap between abstract theory and engineering practice, enhancing cognitive engagement. CONCLUSION: shifting from conventional theoretical instruction to contextual teaching significantly improves students' capacity for probabilistic reasoning and problem-solving. Combining professionally oriented scenarios with software-assisted statistical analysis provides a robust foundation for training agile, highly qualified engineering specialists.