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Консультация № 188780
04.02.2016, 04:36
0.00 руб.
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1
Здравствуйте! У меня возникли сложности с таким вопросом:
Задан закон распределения вероятностей значений дискретной случайной величины X:
Х 5,0 7,0 9,0 11,0 13,0 15,0
P(X) 0,30 0,20 0,15 ? 0,10 0,10.
Найдите вероятность того, что значение х случайной величины Х превысит число 9. Вычислите среднеквадратичное отклонение σ(Х) случайной величины Х.
Спасибо.
Задан закон распределения вероятностей значений дискретной случайной величины X:
Х 5,0 7,0 9,0 11,0 13,0 15,0
P(X) 0,30 0,20 0,15 ? 0,10 0,10.
Найдите вероятность того, что значение х случайной величины Х превысит число 9. Вычислите среднеквадратичное отклонение σ(Х) случайной величины Х.
Спасибо.
Обсуждение
04.02.2016, 09:08
общий
это ответ
Здравствуйте, boltunoff-kati!
1. Находим вероятность p(X=11,0)=p(11,0) того, что дискретная случайная величина примет значение x=11,0:
2. Находим вероятность p(X>9,0) того, что дискретная случайная величина X превысит число 9:
3. Находим математическое ожидание MX дискретной случайной величины X:
4. Находим дисперсию DX дискретной случайной величины X:
5. Находим среднее квадратическое отклонение [$963$]X случайной величины X:
С уважением.
1. Находим вероятность p(X=11,0)=p(11,0) того, что дискретная случайная величина примет значение x=11,0:
p(11,0)=1-(p(5,0)+p(7,0)+p(9,0)+p(13,0)+p(15,0))=1-(0,30+0,20+0,15+0,10+0,10)=1-0,85=0,15.
2. Находим вероятность p(X>9,0) того, что дискретная случайная величина X превысит число 9:
p(X>9,0)=p(11,0)+p(13,0)+p(15,0)=0,15+0,10+0,10=0,35.
3. Находим математическое ожидание MX дискретной случайной величины X:
MX=[$8721$][sub]k[/sub] x[sub]k[/sub]p[sub]k[/sub]=5,0*0,30+7,0*0,20+9,0*0,15+11,0*0,15+13,0*0,10+15,0*0,10=8,7.
4. Находим дисперсию DX дискретной случайной величины X:
DX=[$8721$][sub]k[/sub] (x[sub]k[/sub]-MX)[sup]2[/sup]p[sub]k[/sub]=
=(5,0-8,7)[sup]2[/sup]*0,30+(7,0-8,7)[sup]2[/sup]*0,20+(9,0-8,7)[sup]2[/sup]*0,15+(11,0-8,7)[sup]2[/sup]*0,15+(13,0-8,7)[sup]2[/sup]*0,10+(15,0-8,7)[sup]2[/sup]*0,10=11,61.
5. Находим среднее квадратическое отклонение [$963$]X случайной величины X:
[$963$]X=[$8730$](DX)=[$8730$]11,61[$8776$]3,41.
С уважением.
5
Спасибо!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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