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Консультация № 188197
15.11.2015, 13:16
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
В сборной команде института по стрельбе 18 человек. Из них 8 перворазрядников.Наудачу выбирают 3-х членов сборной.Найти закон распределения числа перворазрядников среди выбранных,функцию распределения F(x),построить её график и найти P(0<x<3)
В сборной команде института по стрельбе 18 человек. Из них 8 перворазрядников.Наудачу выбирают 3-х членов сборной.Найти закон распределения числа перворазрядников среди выбранных,функцию распределения F(x),построить её график и найти P(0<x<3)
Обсуждение
17.11.2015, 05:24
общий
это ответ
Здравствуйте, Никита!
Воспользуемся общей формулой: если имеется n объектов, распределённые по k группам, содержащим соответственно n[sub]1[/sub], n[sub]2[/sub],...n[sub]k[/sub] объектов (n[sub]1[/sub] + n[sub]2[/sub] + ... + n[sub]k[/sub] = n), и производится выборка m объектов (m[$8804$]n), то вероятность того, что среди них будет m[sub]1[/sub] объектов из первой группы, m[sub]2[/sub] - из второй,... m[sub]k[/sub] из k-ой группы (m[sub]1[/sub] + m[sub]2[/sub] + ... + m[sub]k[/sub] = m), равна
В данном случае n = 18, k = 2 (две группы - перворазрядники и остальные), n[sub]1[/sub] = 8 (число перворазрядников), n[sub]2[/sub] = 10 (число остальных), m = 3 (число выбранных). Число перворазрядников среди выбранных m[sub]1[/sub] может принимать значения 0, 1, 2, 3 с вероятностями:
Соответственно, функция распределения будет иметь вид
Тогда P(0<x<3) = F(3-0) - F(0+) = 95/102 - 15/102 = 80/102 [$8776$] 0.784.
Воспользуемся общей формулой: если имеется n объектов, распределённые по k группам, содержащим соответственно n[sub]1[/sub], n[sub]2[/sub],...n[sub]k[/sub] объектов (n[sub]1[/sub] + n[sub]2[/sub] + ... + n[sub]k[/sub] = n), и производится выборка m объектов (m[$8804$]n), то вероятность того, что среди них будет m[sub]1[/sub] объектов из первой группы, m[sub]2[/sub] - из второй,... m[sub]k[/sub] из k-ой группы (m[sub]1[/sub] + m[sub]2[/sub] + ... + m[sub]k[/sub] = m), равна
В данном случае n = 18, k = 2 (две группы - перворазрядники и остальные), n[sub]1[/sub] = 8 (число перворазрядников), n[sub]2[/sub] = 10 (число остальных), m = 3 (число выбранных). Число перворазрядников среди выбранных m[sub]1[/sub] может принимать значения 0, 1, 2, 3 с вероятностями:
Соответственно, функция распределения будет иметь вид
Тогда P(0<x<3) = F(3-0) - F(0+) = 95/102 - 15/102 = 80/102 [$8776$] 0.784.
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