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Консультация № 187032

23.12.2012, 18:21

91.28 руб.

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Образование

Уважаемые эксперты! Пожалуйста, ответьте на вопрос:

[size=4]ЗАДАЧА №3

n=23[/size]

Обсуждение

давно

Орловский Дмитрий

Мастер-Эксперт
319965
1463

23.12.2012, 18:32

общий

это ответ

Здравствуйте, Посетитель - 395735!
Смотрите ответ на эту задачу в вопросе 186979, в котором нужно взять n=23.

давно

Профессор
323606
198

23.12.2012, 18:53

общий

это ответ

Здравствуйте, Посетитель - 395735!
Найдём С из условия

Случайная величина Х имеет равномерное распределение
f(x)=1/46 при х∈[-23, 23]; f(x)=0 при х∉[-23, 23].
Её математическое ожидание M(X)=(a+b)/2=(-23+23)/2=0, дисперсия D(X)=((b-a)²)/12=((23-(-23))^2)/12=529/3.
Случайная величина Y имеет показательное распределение
f(у)=(23/2)е^(-23/2)у при у>0; f(y)=0 при y≤0.
Параметр этого распределения λ=23/2.
Математическое ожидание M(Y)=1/λ=2/23, дисперсия D(Y)=1/λ=2/23.
Используя свойства математического ожидания и дисперсии, находим:
M(Z)=M(X/46-69Y)=(1/46)M(X)-69M(Y)=0/46-69·(2/23)=-6.
D(Z)=D(X/46-69Y)=(1/46)²D(X)+69²D(Y)=(1/2116)[$183$](529/3)+4761[$183$](4/529)=1/12+36=433/12.

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