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Консультация № 200788
05.05.2021, 07:45
0.00 руб.
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1
1
Здравствуйте уважаемые эксперты! Пожалуйста, помогите с задачей:
Величины
и 
распределены по показательному закону распределения с параметрами ~E(9), ~E(6) .
Найти характеристическую функцию
, если и - независимы..
Я пытался решать её следующим образом:
; 
;
И отсюда получаем, что:
Подскажите пожалуйста в чем я мог ошибиться.
С уважением, Артем.
Величины
и распределены по показательному закону распределения с параметрами ~E(9), ~E(6) .Найти характеристическую функцию
, если и - независимы..Я пытался решать её следующим образом:
; ;И отсюда получаем, что:
Подскажите пожалуйста в чем я мог ошибиться.
С уважением, Артем.
Обсуждение
05.05.2021, 21:37
общий
это ответ
Здравствуйте, Artem!
Будем считать очевидным, что если случайные величины и независимы, то и случайные величины 
и 
независимы.
Для решения задачи воспользуемся следующими фактами:
1) если
где 
и 
-- постоянные, то 
[1, с. 141];
2) характеристическая функция суммы двух независимых случайных величин
и 
равна произведению их характеристических функций: 
[1, с. 142];
3) если случайная величина имеет показательное распределение с параметром 
то для неё характеристическая функция имеет вид 
[2, с. 327].
Тогда
Литература
1. Письменный Д. Т. Конспект лекций по теории вероятностей, математической статистике и случайным процессам. -- М.: Айрис-пресс, 2007.
2. Вентцель Е. С., Овчаров Л. А. Теория вероятностей и её инженерные приложения. -- М.: Высшая школа, 2000.
Будем считать очевидным, что если случайные величины
и независимы, то и случайные величины и независимы.Для решения задачи воспользуемся следующими фактами:
1) если
где и -- постоянные, то [1, с. 141];2) характеристическая функция суммы двух независимых случайных величин
и равна произведению их характеристических функций: [1, с. 142];3) если случайная величина
имеет показательное распределение с параметром то для неё характеристическая функция имеет вид [2, с. 327].Тогда
Литература
1. Письменный Д. Т. Конспект лекций по теории вероятностей, математической статистике и случайным процессам. -- М.: Айрис-пресс, 2007.
2. Вентцель Е. С., Овчаров Л. А. Теория вероятностей и её инженерные приложения. -- М.: Высшая школа, 2000.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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