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Задать вопрос экспертам

Консультация № 188447

18.12.2015, 11:06

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Образование

Здравствуйте, уважаемые эксперты! Прошу Вас помочь решить данное задание, искал что-то подобное, нигде не нашел:

Обсуждение

давно

Коцюрбенко Алексей Владимирович

Старший Модератор
312929
1973

23.12.2015, 04:53

общий

это ответ

Здравствуйте, hwnlJc4c!

а) Вероятность попадания случайной величины [$958$] в интервал (a, b) равна

где F - её функция распределения. Для случайной величины, распределённой нормально с математическим ожиданием a = M[$958$] и среднеквадратическим отклонением [$963$] , функция распределения имеет вид

где [$934$](x) - стандартная функция распределения для нормального закона. В данном случае a = 5, следовательно

Так как для стандартной функции распределения [$934$](-x) = 1 - [$934$](x), то

откуда

Значение 0.99865 функция [$934$](x) принимает при x = 3, то есть 3/[$963$] = 3, откуда [$963$] = 1 и [$963$][sup]2[/sup] = 1.

б) Вероятность того, что случайная величина не превышает некоторого значения, равна функции распределения для этого значения. В данном случае

(с точностью до пяти знаков после запятой).

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