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Консультация № 177746
08.04.2010, 14:42
40.81 руб.
0
1
1
Добрый день! Помогите, пожалуйста, с решением ещё одной задачи по теории вероятностей:
Спасибо!
Спасибо!
Обсуждение
Неизвестный
09.04.2010, 02:23
общий
это ответ
Здравствуйте, MrSpencer.
f(x)={0, x<0
a*x+b, 0[$8804$]x[$8804$]0.4
0, x>0.4}
Найдем a и b> так, чтобы [$8747$]-[$8734$]+[$8734$]f(x)dx=1
[$8747$]-[$8734$]+[$8734$]f(x)dx=[$8747$]00.4(a*x+b)dx=((a/2)*x2+b*x)|02/5=(2/25)*a+(2/5)*b=1
а также f(2/5)=(2/5)*a+b=0
Получим a=-(25/2) , b= 5
f(x)={0, x<0
-(25/2)x+5, 0[$8804$]x[$8804$]0.4
0, x>0.4}
[$8747$]f(x)dx=(-25/4)*x2+5*x+C
F(x)={0, x<0
(-25/4)*x2+5*x, 0[$8804$]x[$8804$]0.4
1, x>0.4}
График F(x):
P(0.2;0.4)=F(0.4)-F(0.2)=1-3/4=1/4=0.25
mx=[$8747$]-[$8734$]+[$8734$]x*f(x)dx=[$8747$]02/5(5*x-(25/2)*x2)dx=2/5-4/15=2/15
[$945$]2=[$8747$]-[$8734$]+[$8734$]x2*f(x)dx=[$8747$]02/5(5*x2-(25/2)*x3)dx=8/75-2/25=2/75
dx=[$945$]2-(mx)2=2/75-4/225=2/225
f(x)={0, x<0
a*x+b, 0[$8804$]x[$8804$]0.4
0, x>0.4}
Найдем a и b> так, чтобы [$8747$]-[$8734$]+[$8734$]f(x)dx=1
[$8747$]-[$8734$]+[$8734$]f(x)dx=[$8747$]00.4(a*x+b)dx=((a/2)*x2+b*x)|02/5=(2/25)*a+(2/5)*b=1
а также f(2/5)=(2/5)*a+b=0
Получим a=-(25/2) , b= 5
f(x)={0, x<0
-(25/2)x+5, 0[$8804$]x[$8804$]0.4
0, x>0.4}
[$8747$]f(x)dx=(-25/4)*x2+5*x+C
F(x)={0, x<0
(-25/4)*x2+5*x, 0[$8804$]x[$8804$]0.4
1, x>0.4}
График F(x):
P(0.2;0.4)=F(0.4)-F(0.2)=1-3/4=1/4=0.25
mx=[$8747$]-[$8734$]+[$8734$]x*f(x)dx=[$8747$]02/5(5*x-(25/2)*x2)dx=2/5-4/15=2/15
[$945$]2=[$8747$]-[$8734$]+[$8734$]x2*f(x)dx=[$8747$]02/5(5*x2-(25/2)*x3)dx=8/75-2/25=2/75
dx=[$945$]2-(mx)2=2/75-4/225=2/225
5
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