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Консультация № 173953
04.11.2009, 08:36
0.00 руб.
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Здравствуйте, уважаемые эксперты! Возникли проблемы с задачами по терии вероятностей, требуется Ваша помощь в решении хотя бы одной из них. Вот формулировка задачи:
Случайная величина X задана функцией распределения (интегральной функцией) F(x). Найти плотность вероятности (дифференциальную функцию), мат. ожидание и дисперсию. Построить график интегральной и дифференциальной функций. Найти вероятность попадания случ. величины на указанный промежуток: [2.5;3]
F(x) = |0, x<=2
|1/2*x-1, 2<x<=4
|1, x>4
Среди других вопросов я нашел решение похожей задачи, но оно для меня абсолютно непонятное. Жду Вашей помощи.
Случайная величина X задана функцией распределения (интегральной функцией) F(x). Найти плотность вероятности (дифференциальную функцию), мат. ожидание и дисперсию. Построить график интегральной и дифференциальной функций. Найти вероятность попадания случ. величины на указанный промежуток: [2.5;3]
F(x) = |0, x<=2
|1/2*x-1, 2<x<=4
|1, x>4
Среди других вопросов я нашел решение похожей задачи, но оно для меня абсолютно непонятное. Жду Вашей помощи.
Обсуждение
Неизвестный
09.11.2009, 06:56
общий
Неужели мне так никто и не поможет? Все же надеюсь на помощь, может быть найдется добрый человек...
29.08.2022, 10:05
общий
это ответ
Здравствуйте, Quikk!
Пусть непрерывная случайная величина
задана интегральной функцией распределения
Тогда дифференциальная функция распределения суть
то есть случайная величина распределена равномерно на промежутке 
Поэтому её математическое ожидание равно
дисперсия равна
Эти же величины можно вычислить иначе:
При этом
или
Графики функций
и 
показаны в прикреплённых файлах.
Пусть непрерывная случайная величина
задана интегральной функцией распределенияТогда дифференциальная функция распределения суть
то есть случайная величина
распределена равномерно на промежутке Поэтому её математическое ожидание равнодисперсия равна
Эти же величины можно вычислить иначе:
При этом
или
Графики функций
и показаны в прикреплённых файлах.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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