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Консультация № 200669
17.04.2021, 09:29
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Производится n=1000 независимых испытаний, в каждом из которых событие A наблюдается с вероятностью 1/4. Случайная величина X–число появлений A в nиспытаниях. Найти интервал, симметричный относительно математического ожидания, в который X попадет с вероятностью 0.95
Производится n=1000 независимых испытаний, в каждом из которых событие A наблюдается с вероятностью 1/4. Случайная величина X–число появлений A в nиспытаниях. Найти интервал, симметричный относительно математического ожидания, в который X попадет с вероятностью 0.95
Обсуждение
18.04.2021, 08:32
общий
это ответ
Здравствуйте, kit!
В тех случаях, когда число испытаний
велико, а вероятность 
не близка к нулю 
для вычисления биномиальных вероятностей используют теоремы Муавра -- Лапласа. Воспользуемся интегральной теоремой:
При этом на практике обычно используют формулу
где
-- нормированная функция Лапласа.
В Вашем случае
Следовательно, искомый интервал:
Литература
Письменный Д. т. Конспект лекций по теории вероятностей, математической статистике и случайным процессам. -- М.: Айрис-пресс, 2007. -- 288 с.
В тех случаях, когда число испытаний
велико, а вероятность не близка к нулю для вычисления биномиальных вероятностей используют теоремы Муавра -- Лапласа. Воспользуемся интегральной теоремой:При этом на практике обычно используют формулу
где
-- нормированная функция Лапласа.В Вашем случае
Следовательно, искомый интервал:
Литература
Письменный Д. т. Конспект лекций по теории вероятностей, математической статистике и случайным процессам. -- М.: Айрис-пресс, 2007. -- 288 с.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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