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1 законы больших чисел
законы больших чисел
Фундаментальные законы математической статистики, говорящие, что при достаточно большом количестве испытаний обобщающие характеристики выборок случайных величин как бы теряют свой случайный характер, при сложении достаточно большого количества случайных величин их разнонаправленные отклонения взаимно погашаются и так далее. Наиболее известны среди З.б.ч. — теорема Бернулли (по ней обосновывается возможность выбора частоты осуществления некоторого события в качестве оценки вероятности этого события), теорема Ляпунова (иначе — центральная предельная теорема), которая говорит, что распределение суммы n произвольно распределенных и взаимно независимых случайных величин при n®? стремится к нормальному распределению, если вклад отдельных слагаемых в сумму равномерно мал, а также теорема Чебышева, позволяющая при большом количестве случайных величин использовать среднее арифметическое выборки в качестве оценки математического ожидания всей генеральной совокупности рассматриваемых величин.
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