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Консультация № 180525
31.10.2010, 19:57
0.00 руб.
0
8
1
Помогите, пожалуйста, решить задачу:
"
Случайные величины ξ и η независимы и нормально распределены с Mξ =Mη =0, Dξ =Dη =1. Найдите:
1) вероятность того, что случайная точка (ξ, η) попадет в область S;
2) вероятность события (λ принадлежит A), где λ – линейная функция случайных величин ξ и η;
3) среднее квадратичное отклонение λ.
S={(x,y): |x+y|<=1, sign(x) = sign(y)}, λ=ξ+2η, A={0<=x<=2}.
".
"
Случайные величины ξ и η независимы и нормально распределены с Mξ =Mη =0, Dξ =Dη =1. Найдите:
1) вероятность того, что случайная точка (ξ, η) попадет в область S;
2) вероятность события (λ принадлежит A), где λ – линейная функция случайных величин ξ и η;
3) среднее квадратичное отклонение λ.
S={(x,y): |x+y|<=1, sign(x) = sign(y)}, λ=ξ+2η, A={0<=x<=2}.
".
Обсуждение
05.11.2010, 09:36
общий
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Здравствуйте!
Ваш ответ таковым является не вполне.
Вам следовало либо оказать конкретную помощь, либо указание о полярных координатах поместить в мини-форуме вопроса. Кроме того, вопрос помещён в рассылку "Теория вероятностей", потому что именно этот раздел математики изучает вопросы распределения случайных величин.
С уважением.
Ваш ответ таковым является не вполне.
Вам следовало либо оказать конкретную помощь, либо указание о полярных координатах поместить в мини-форуме вопроса. Кроме того, вопрос помещён в рассылку "Теория вероятностей", потому что именно этот раздел математики изучает вопросы распределения случайных величин.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
05.11.2010, 17:45
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Вы вникли в физический смысл полученного Вами ответа на первый пункт задания? И какова, по-Вашему, вероятность попадания точки в одну полуобласть области S? 
Об авторе:
Facta loquuntur.
Facta loquuntur.
05.11.2010, 17:56
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Формула точно правильна. Возможно, что-то не учел или допустил ошибку при вычислении интеграла. В теории вероятностей области для нормального распределения, как правило, прямоугольные. А тут треугольная. Ни в какой книжке по ТВ не видел подобного примера (касательно области). Ведь интеграл выражается через протабулированную функцию Лапласа, а не через элементарные функции.
05.11.2010, 22:23
общий
это ответ
Здравствуйте, Посетитель - 342555!
Предлагаю Вам следующее решение задачи.
С уважением.
Предлагаю Вам следующее решение задачи.
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
05.11.2010, 22:24
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Всё гораздо проще, если только я сам не ошибаюсь. Смотрите, пожалуйста, мой ответ...
Об авторе:
Facta loquuntur.
Facta loquuntur.
05.11.2010, 23:17
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Спасибо за верный ответ. Век живи - век учись. Автора книги не подскажете?
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