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Консультация № 179911
11.09.2010, 18:46
41.22 руб.
0
1
1
И еще одна задача.
В команде 16 спортсменов, из которых 10 перворазрядников. Наудачу выбирают двух спортсменов. Построить ряд распределения и многоугольник распределения дискретной случайной величины Х – числа перворазрядников среди выбранных. Найти М(Х) и Д(Х).
В команде 16 спортсменов, из которых 10 перворазрядников. Наудачу выбирают двух спортсменов. Построить ряд распределения и многоугольник распределения дискретной случайной величины Х – числа перворазрядников среди выбранных. Найти М(Х) и Д(Х).
Обсуждение
11.09.2010, 19:47
общий
это ответ
Здравствуйте, alya_koshka.
Имеем гипергеометрическое распределение. Вероятность того, что окажется k перворазрядников
p(k)=C10k*C62-k/C162
Соответственно
p(0)=C100*C62/C162=1/8
p(1)=C101*C61/C162=1/2
p(2)=C102*C60/C162=3/8
Математическое ожидание
MX=0*p(0)+1*p(1)+2*p(2)=5/4
Математическое ожидание X2
MX2=0*p(0)+1*p(1)+4*p(2)=2
Дисперсия
DX=M(X2)-(MX)2=39/16
Имеем гипергеометрическое распределение. Вероятность того, что окажется k перворазрядников
p(k)=C10k*C62-k/C162
Соответственно
p(0)=C100*C62/C162=1/8
p(1)=C101*C61/C162=1/2
p(2)=C102*C60/C162=3/8
Математическое ожидание
MX=0*p(0)+1*p(1)+2*p(2)=5/4
Математическое ожидание X2
MX2=0*p(0)+1*p(1)+4*p(2)=2
Дисперсия
DX=M(X2)-(MX)2=39/16
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