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Консультация № 185921
28.04.2012, 18:29
66.21 руб.
0
4
2
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Известна плотность вероятности случайной величины: https://rfpro.ru/upload/8021
Построить кривую вероятности. Найти вероятности событий: А - случайная величина примет только положительные значения;
В – случайная величина попадет в интервал, длиной в два средних квадратических отклонения, симметричный относительно математического ожидания.
Известна плотность вероятности случайной величины: https://rfpro.ru/upload/8021
Построить кривую вероятности. Найти вероятности событий: А - случайная величина примет только положительные значения;
В – случайная величина попадет в интервал, длиной в два средних квадратических отклонения, симметричный относительно математического ожидания.
Обсуждение
28.04.2012, 19:39
общий
это ответ
Здравствуйте, Марина!
Кривая вероятностей для нормально распределенной случайной величины Х с плотностью вероятности
имеет вид
Асимптотой кривой при х[$8594$][$177$][$8734$] является ось х. Точка максимума (-2, 1/([$963$][$8730$]2[$8719$])).
Вероятности событий найдем, используя формулы попадания в заданный интервал для нормально распределенной случайной величины (m=-2, [$963$]=1,5) и табличные значения функции Лапласа Ф(х).
P(A)=P(X>0)=P(0<X<[$8734$])=Ф([$8734$])-Ф((0-m)/[$963$])=0,5-Ф(2/1,5)=0,5-Ф(1,33)=0,5-0,4082=0,0918,
Р(В)=Р(m-[$963$]<Х<m+[$963$])=P(|X-m|<[$963$])=2Ф([$963$]/[$963$])=2Ф(1)=2*0,3413=0,6826.
Кривая вероятностей для нормально распределенной случайной величины Х с плотностью вероятности
имеет вид
Асимптотой кривой при х[$8594$][$177$][$8734$] является ось х. Точка максимума (-2, 1/([$963$][$8730$]2[$8719$])).
Вероятности событий найдем, используя формулы попадания в заданный интервал для нормально распределенной случайной величины (m=-2, [$963$]=1,5) и табличные значения функции Лапласа Ф(х).
P(A)=P(X>0)=P(0<X<[$8734$])=Ф([$8734$])-Ф((0-m)/[$963$])=0,5-Ф(2/1,5)=0,5-Ф(1,33)=0,5-0,4082=0,0918,
Р(В)=Р(m-[$963$]<Х<m+[$963$])=P(|X-m|<[$963$])=2Ф([$963$]/[$963$])=2Ф(1)=2*0,3413=0,6826.
5
28.04.2012, 19:48
общий
Адресаты:
Добрый вечер! 
Ваши вычисления Р(В) задают вероятность отклонения Х от m на величину 2[$963$], т.е. попадание Х в интервал длиной 4[$963$], симметричный относительно мат.ожидания. Или я ошибаюсь?
Ваши вычисления Р(В) задают вероятность отклонения Х от m на величину 2[$963$], т.е. попадание Х в интервал длиной 4[$963$], симметричный относительно мат.ожидания. Или я ошибаюсь?
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