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Консультация № 182568
20.03.2011, 21:55
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Здравствуйте! Прошу помощи в следующем вопросе:
Последовательность независимых случайных величин {[$958$]k} задана законом распределения:
[$958$]k -3^2 0 3^2
Р 1/3 1/3 1/3
Применимы ли теоремы Чебышева и Хинчина?
Заранее благодарю, Уважаемые эксперты
Приложение:
[$958$] - греч буква Кси
Последовательность независимых случайных величин {[$958$]k} задана законом распределения:
[$958$]k -3^2 0 3^2
Р 1/3 1/3 1/3
Применимы ли теоремы Чебышева и Хинчина?
Заранее благодарю, Уважаемые эксперты
Приложение:
[$958$] - греч буква Кси
Обсуждение
Неизвестный
20.03.2011, 22:49
общий
это ответ
Здравствуйте, Петров Федор Степанович!
Теоремы Чебышева, теорему Хинчина (закон больших чисел) можно применять к последовательности независимых одинаково распределенных случайных величин, если существует конечное математическое ожидание каждой случайной величины и если дисперсии этих величин ограничены в совокупности.
Имеем: мат. ожидание a=M[[$958$][sub]k[/sub]]=-9*1/3+0*1/3+9*1/3=0;
дисперсия D=M[([$958$][sub]k[/sub]-a)[sup]2[/sup]]=81*1/3+0*1/3+81*1/3=81*2/3=54.
Как видно, все условия выполняются.
Ответ: применимы.
Теоремы Чебышева, теорему Хинчина (закон больших чисел) можно применять к последовательности независимых одинаково распределенных случайных величин, если существует конечное математическое ожидание каждой случайной величины и если дисперсии этих величин ограничены в совокупности.
Имеем: мат. ожидание a=M[[$958$][sub]k[/sub]]=-9*1/3+0*1/3+9*1/3=0;
дисперсия D=M[([$958$][sub]k[/sub]-a)[sup]2[/sup]]=81*1/3+0*1/3+81*1/3=81*2/3=54.
Как видно, все условия выполняются.
Ответ: применимы.
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