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Консультация № 199740
28.11.2020, 21:23
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Система непрерывных случайных величин (Х,У) имеет постоянную плотность вероятностей f(х,у) в заданной области. Являются ли случайные величины Х,У независимыми? Если нет, то определить условные математические ожидания случайных величин Х,У.
Исходные данные к задачам: Внутренность квадрата с вершинами в точках (0,0), (0,1), (1,0), (1,1).
Спасибо
Система непрерывных случайных величин (Х,У) имеет постоянную плотность вероятностей f(х,у) в заданной области. Являются ли случайные величины Х,У независимыми? Если нет, то определить условные математические ожидания случайных величин Х,У.
Исходные данные к задачам: Внутренность квадрата с вершинами в точках (0,0), (0,1), (1,0), (1,1).
Спасибо
Обсуждение
05.12.2020, 20:28
общий
это ответ
Здравствуйте, erorr2!
Пусть D - указанный в условии квадрат, тогда
Исходя из условия нормировки
получаем
то есть
Тогда плотности вероятности случайных величин X и Y будут равны
и так как f(x, y) = f(x)f(y), то X и Y - независимые случайные величины.
Пусть D - указанный в условии квадрат, тогда
Исходя из условия нормировки
получаем
то есть
Тогда плотности вероятности случайных величин X и Y будут равны
и так как f(x, y) = f(x)f(y), то X и Y - независимые случайные величины.
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