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Консультация № 202627
17.04.2022, 12:53
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Задана функция распределения непрерывной СВ X (на фото).
Найдите: коэффициент a; плотность распределения f(x) СВ X; вероятность попадания СВ X в отрезок [2;4]; вероятность того, что при двух независимых испытаниях СВ X примет значение большее 2 хотя бы один раз; математическое ожидание и дисперсию.
Задана функция распределения непрерывной СВ X (на фото).
Найдите: коэффициент a; плотность распределения f(x) СВ X; вероятность попадания СВ X в отрезок [2;4]; вероятность того, что при двух независимых испытаниях СВ X примет значение большее 2 хотя бы один раз; математическое ожидание и дисперсию.
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Обсуждение
18.04.2022, 21:10
общий
это ответ
Здравствуйте, svrvsvrv!
При
согласно свойству нормировки дифференциальной функции распределения, имеем
Поэтому дифференциальная функция, или плотность, распределения такова:
Вероятность попадания случайной величины
в отрезок 
составляет
Такова и вероятность того, что случайная величина не меньше (и больше) двух. Поэтому вероятность того, что при двух независимых испытаниях она примет значение, большее двух, составляет
Вычислим математическое ожидание случайной величины
а также её дисперсию:
При
согласно свойству нормировки дифференциальной функции распределения, имеемПоэтому дифференциальная функция, или плотность, распределения такова:
Вероятность попадания случайной величины
в отрезок составляетТакова и вероятность того, что случайная величина
не меньше (и больше) двух. Поэтому вероятность того, что при двух независимых испытаниях она примет значение, большее двух, составляетВычислим математическое ожидание случайной величины
а также её дисперсию:
5
Премного благодарен.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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