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Консультация № 183310
24.05.2011, 12:35
49.06 руб.
0
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Нормально распределенная величина Х задана своими параметрами [$945$] (математическоеожидание), [$963$] (среднеквадратическое отклонение). Требуется написать плотность вероятности и схематические изобразить ее график; найти вероятность того, что Х принимет значение из интервала (а, [$946$]); найти вероятность того, что Х отклонится (по модулю) от а, но не более чем на б; применяя правило " трех сигм" найти значение случайной величины Х.
[$945$]=10
б=2
[$963$]=4
а=5
[$946$]=12
Нормально распределенная величина Х задана своими параметрами [$945$] (математическоеожидание), [$963$] (среднеквадратическое отклонение). Требуется написать плотность вероятности и схематические изобразить ее график; найти вероятность того, что Х принимет значение из интервала (а, [$946$]); найти вероятность того, что Х отклонится (по модулю) от а, но не более чем на б; применяя правило " трех сигм" найти значение случайной величины Х.
[$945$]=10
б=2
[$963$]=4
а=5
[$946$]=12
Обсуждение
24.05.2011, 19:26
общий
это ответ
Здравствуйте, Посетитель - 364448!
Плотность вероятности
p(x)=(1/([$963$][$8730$](2Pi)))e^(-(x-[$945$])2/(2[$963$]2)=0,0997e^(-(x-10)2/32)
График:
P(a<x<[$946$])=Ф(([$946$]-[$945$])/[$963$]))-Ф((a-[$945$])/[$963$]))
где Ф - функция Лапласа.
В нашем случае
([$946$]-[$945$])/[$963$])=(12-10)/4=1/2=0,5
(a-[$945$])/[$963$])=(5-10)/4=-5/4=-1,25
Учитывая нечетность функции Лапласа, находим по таблице
Ф(0,5)=0,1915
Ф(-1,25)=-Ф(1,25)=-0,3944
P(a<x<[$946$])=P(5<x<12)=0,1915-(-0,3944)=0,1915+0,3944=0,5859
P(|x-[$945$]|<б)=2Ф(б/[$963$])
В нашем случае находим по таблице
P(|x-[$945$]|<б)=P(|x-10|<2)=2Ф(2/4)=2Ф(0,5)=2*0,1915=0,3830
Согласно правилу трех сигм значение случайной величины следует ожидать в интервале
([$945$]-3[$963$];[$945$]+3[$963$])
В нашем случае ([$945$]=10, [$963$]=4), это интервал (-2;22)
Плотность вероятности
p(x)=(1/([$963$][$8730$](2Pi)))e^(-(x-[$945$])2/(2[$963$]2)=0,0997e^(-(x-10)2/32)
График:
P(a<x<[$946$])=Ф(([$946$]-[$945$])/[$963$]))-Ф((a-[$945$])/[$963$]))
где Ф - функция Лапласа.
В нашем случае
([$946$]-[$945$])/[$963$])=(12-10)/4=1/2=0,5
(a-[$945$])/[$963$])=(5-10)/4=-5/4=-1,25
Учитывая нечетность функции Лапласа, находим по таблице
Ф(0,5)=0,1915
Ф(-1,25)=-Ф(1,25)=-0,3944
P(a<x<[$946$])=P(5<x<12)=0,1915-(-0,3944)=0,1915+0,3944=0,5859
P(|x-[$945$]|<б)=2Ф(б/[$963$])
В нашем случае находим по таблице
P(|x-[$945$]|<б)=P(|x-10|<2)=2Ф(2/4)=2Ф(0,5)=2*0,1915=0,3830
Согласно правилу трех сигм значение случайной величины следует ожидать в интервале
([$945$]-3[$963$];[$945$]+3[$963$])
В нашем случае ([$945$]=10, [$963$]=4), это интервал (-2;22)
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