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Консультация № 181623
26.12.2010, 14:24
52.69 руб.
0
2
1
Здравствуйте, уважаемые эксперты! Прошу Вас ответить на следующий вопрос:
Случайная величина [$958$] подчиняется закону распределения Коши p[$958$](x) = 1/(pi(1+x^2)) . Найти плотность вероятности случайной величины [$627$] = 1 - [$958$]^3 .
Случайная величина [$958$] подчиняется закону распределения Коши p[$958$](x) = 1/(pi(1+x^2)) . Найти плотность вероятности случайной величины [$627$] = 1 - [$958$]^3 .
Обсуждение
26.12.2010, 16:01
общий
Если функция f(x) имеет обратную g(x), то плотность распределения ɳ=f(ξ)находят по формуле
pɳ(x)=pξ(g(x))|g'(x)|
Найдем обратную к функции y=1-x^3
x^3=1-y
x=3[$8730$](1-y)
g(x)=3[$8730$](1-x)
g'(x)=-1/3(1-x)^(-2/3)
Так как g - не возрастающая, а убывающая
pɳ(x)=pξ(g(x))|g'(x)|=1/(3п(1+(1-x)^2/3)) (1-x)^(2/3))
pɳ(x)=pξ(g(x))|g'(x)|
Найдем обратную к функции y=1-x^3
x^3=1-y
x=3[$8730$](1-y)
g(x)=3[$8730$](1-x)
g'(x)=-1/3(1-x)^(-2/3)
Так как g - не возрастающая, а убывающая
pɳ(x)=pξ(g(x))|g'(x)|=1/(3п(1+(1-x)^2/3)) (1-x)^(2/3))
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