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Консультация № 184529
23.11.2011, 00:57
61.31 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на самый страшный вопрос:
Обсуждение
23.11.2011, 01:25
общий
это ответ
Здравствуйте, lexmod!
Плотности вероятности составляющих:
Математические ожидания:
Идентично
Плотности вероятности составляющих:
Математические ожидания:
Идентично
23.11.2011, 01:46
общий
это ответ
Здравствуйте, lexmod!
Если f(x, y) = (sin (x + y))/2 при 0 [$8804$] x [$8804$] п/2, 0 [$8804$] y [$8804$] п/2, а иначе f(x, y) = 0, то
M(X) = 0[$8747$]п/20[$8747$]п/2x [$183$] (sin (x + y))dxdy/2 = 1/2 [$183$] 0[$8747$]п/2xdx0[$8747$]п/2(sin (x + y))dy = 1/2 [$183$] 0[$8747$]п/2xdx [$183$] (-cos (x + y))|0п/2 =
= -1/2 [$183$] 0[$8747$]п/2xdx [$183$] (cos (x + п/2) - cos x) = -1/2 [$183$] 0[$8747$]п/2xdx [$183$] (-sin x - cos x) = 1/2 [$183$] 0[$8747$]п/2xdx [$183$] (sin x + cos x) =
= 1/2 [$183$] (0[$8747$]п/2x [$183$] sin x [$183$] dx + 0[$8747$]п/2x [$183$] cos x [$183$] dx) = 1/2 [$183$] (-x [$183$] cos x + x [$183$] sin x)|0п/2 + 1/2 [$183$] (0[$8747$]п/2cos x [$183$] dx - 0[$8747$]п/2sin x [$183$] dx) =
= 1/2 [$183$] (-п/2 [$183$] cos п/2 + п/2 [$183$] sin п/2) + 1/2 [$183$] (sin x + cos x)|0п/2 =
= п/4 + 1/2 [$183$] (sin п/2 + cos п/2 - (sin 0 + cos 0)) = п/4 + 1/2 [$183$] (1 + 0 - (0 + 1)) = п/4.
Аналогично M(Y) = п/4 в силу перестановочности аргументов x и y.
Ответ: M(X) = M(Y) = п/4.
С уважением.
Если f(x, y) = (sin (x + y))/2 при 0 [$8804$] x [$8804$] п/2, 0 [$8804$] y [$8804$] п/2, а иначе f(x, y) = 0, то
M(X) = 0[$8747$]п/20[$8747$]п/2x [$183$] (sin (x + y))dxdy/2 = 1/2 [$183$] 0[$8747$]п/2xdx0[$8747$]п/2(sin (x + y))dy = 1/2 [$183$] 0[$8747$]п/2xdx [$183$] (-cos (x + y))|0п/2 =
= -1/2 [$183$] 0[$8747$]п/2xdx [$183$] (cos (x + п/2) - cos x) = -1/2 [$183$] 0[$8747$]п/2xdx [$183$] (-sin x - cos x) = 1/2 [$183$] 0[$8747$]п/2xdx [$183$] (sin x + cos x) =
= 1/2 [$183$] (0[$8747$]п/2x [$183$] sin x [$183$] dx + 0[$8747$]п/2x [$183$] cos x [$183$] dx) = 1/2 [$183$] (-x [$183$] cos x + x [$183$] sin x)|0п/2 + 1/2 [$183$] (0[$8747$]п/2cos x [$183$] dx - 0[$8747$]п/2sin x [$183$] dx) =
= 1/2 [$183$] (-п/2 [$183$] cos п/2 + п/2 [$183$] sin п/2) + 1/2 [$183$] (sin x + cos x)|0п/2 =
= п/4 + 1/2 [$183$] (sin п/2 + cos п/2 - (sin 0 + cos 0)) = п/4 + 1/2 [$183$] (1 + 0 - (0 + 1)) = п/4.
Аналогично M(Y) = п/4 в силу перестановочности аргументов x и y.
Ответ: M(X) = M(Y) = п/4.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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