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Консультация № 176886
24.02.2010, 01:31
0.00 руб.
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Здравствуйте уважаемые эксперты, помогите пожалуйста с решением задачи:
Случайная величина X задана функцией распределения (интегральной функцией) F(x). Найти плотность вероятности (дифференциальную функцию, математическое ожидание и дисперсию). Построить графики интегральной и дифференциальной функций.
{0 при x[$8804$](-Пи/2)
F(x)={cos(x) при (-Пи/2)<x[$8804$]0
{1 при x>0
заранее спасибо всем.
Случайная величина X задана функцией распределения (интегральной функцией) F(x). Найти плотность вероятности (дифференциальную функцию, математическое ожидание и дисперсию). Построить графики интегральной и дифференциальной функций.
{0 при x[$8804$](-Пи/2)
F(x)={cos(x) при (-Пи/2)<x[$8804$]0
{1 при x>0
заранее спасибо всем.
Обсуждение
24.02.2010, 16:20
общий
это ответ
Здравствуйте, Мария Романова.
{0 при x≤(-Пи/2)
f(x)={-sin(x) при (-Пи/2)<x≤0
{0 при x>0
Математическое ожидание D[$958$]=[$8747$]-[$8734$][$8734$]xf(x)dx=-[$8747$]-[$960$]/20xsinxdx=-1
Дисперсия E[$958$]=D[$958$]2-(D[$958$])2
D[$958$]2=-[$8747$]-[$8734$][$8734$]x2f(x)dx=-[$8747$]-[$960$]/20x2sinxdx=[$8747$]0[$960$]/2x2sinxdx= -x2cosx+2xsinx+2cosx|0[$960$]/2=[$960$]-2
E[$958$]=[$960$]-3
{0 при x≤(-Пи/2)
f(x)={-sin(x) при (-Пи/2)<x≤0
{0 при x>0
Математическое ожидание D[$958$]=[$8747$]-[$8734$][$8734$]xf(x)dx=-[$8747$]-[$960$]/20xsinxdx=-1
Дисперсия E[$958$]=D[$958$]2-(D[$958$])2
D[$958$]2=-[$8747$]-[$8734$][$8734$]x2f(x)dx=-[$8747$]-[$960$]/20x2sinxdx=[$8747$]0[$960$]/2x2sinxdx= -x2cosx+2xsinx+2cosx|0[$960$]/2=[$960$]-2
E[$958$]=[$960$]-3
24.02.2010, 16:36
общий
это ответ
Здравствуйте, Мария Романова.
Плотность вероятности p(x) получаем дифференцированием функции распределения:
при x<-pi/2 p(x)=0
при -pi/2<x<0 p(x)=-sin x
при x>0 p(x)=0
Математическое ожидание
M=[$8747$](-pi/2)0xp(x)dx=-[$8747$](-pi/2)0x*sin xdx=
(x*cos x-sin x)(-pi/2)0=-1
Второй момент
M2=[$8747$](-pi/2)0x2p(x)dx=-[$8747$](-pi/2)0x2*sin xdx=
(x2*cos x-2x*sin x-2cos x)(-pi/2)0=pi-2
Дисперсия
D=M2-M2=pi-3
Плотность вероятности p(x) получаем дифференцированием функции распределения:
при x<-pi/2 p(x)=0
при -pi/2<x<0 p(x)=-sin x
при x>0 p(x)=0
Математическое ожидание
M=[$8747$](-pi/2)0xp(x)dx=-[$8747$](-pi/2)0x*sin xdx=
(x*cos x-sin x)(-pi/2)0=-1
Второй момент
M2=[$8747$](-pi/2)0x2p(x)dx=-[$8747$](-pi/2)0x2*sin xdx=
(x2*cos x-2x*sin x-2cos x)(-pi/2)0=pi-2
Дисперсия
D=M2-M2=pi-3
Форма ответа
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