DISKRET VA UZLUKSIZ TASODIFIY MIQDORLARNING TAQSIMOT FUNKSIYALARINI TADQIQ ETISH
Keywords:
Kalit so‘zlar: tasodifiy miqdor, taqsimot funksiyasi, ehtimollik massasi, ehtimollik zichligi, matematik kutilma, dispersiya, binomial taqsimot, eksponensial taqsimot, statistik modellashtirish, ehtimollar nazariyasi.Abstract
Annotatsiya
Mazkur maqolada diskret va uzluksiz tasodifiy miqdorlarning taqsimot
funksiyalari, ularning ehtimollik massasi va zichlik funksiyalari bilan bog‘liqligi,
matematik kutilma hamda dispersiya kabi asosiy statistik ko‘rsatkichlar tizimli
ravishda tahlil qilindi. Tadqiqotda ehtimollar nazariyasining rivojlanish bosqichlari,
taqsimot funksiyasining nazariy mazmuni va amaliy modellashtirishdagi o‘rni
yoritildi. Diskret holatda P(X = x_i) = p_i, uzluksiz holatda esa f(x) ≥ 0, ∫f(x)dx = 1 va
F(x) = ∫_-∞^x f(t)dt munosabatlari ilmiy izohlandi. Natijalar qismida binomial va
eksponensial taqsimotlar asosida amaliy hisob-kitoblar bajarilib, taqsimot
funksiyalarining bosqichma-bosqich shakllanishi, ehtimolliklarning yig‘ilishi va
parametrlarning ta’siri jadval hamda grafiklar orqali ko‘rsatildi. Muhokamada diskret
va uzluksiz modeling yondashuvlari solishtirilib, ularning afzalliklari va cheklovlari
muhim statistik xulosalar bilan mustahkamlandi. Tadqiqot natijalari ehtimollik
nazariyasi, statistik tahlil va amaliy modellashtirishni o‘qitish hamda qo‘llashda
foydali nazariy-uslubiy asos bo‘lib xizmat qiladi.
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