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Консультация № 186999
19.12.2012, 23:11
78.80 руб.
20.12.2012, 17:16
0
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Случайная величина Х имеет равномерное распределение. Найти вероятность попадания случайной величины Х в интервал (18;36), если математическое ожидание случайной величины Х равно 18, а среднее квадратическое отклонение
.
Случайная величина Х имеет равномерное распределение. Найти вероятность попадания случайной величины Х в интервал (18;36), если математическое ожидание случайной величины Х равно 18, а среднее квадратическое отклонение
.
Обсуждение
19.12.2012, 23:38
общий
20.12.2012, 17:18
это ответ
Здравствуйте, roover!
Плотность вероятности случайной величины Х, равномерно распределённой в интервале (a, b), задаётся следующим образом:
f(x)=1/(b-a) при х?(a, b); f(x)=0 при х?(a, b).
Её математическое ожидание М(Х)=ab[$8747$]хf(x)dx=(a+b)/2,
дисперсия D(X)=ab[$8747$]х2f(x)dx-(M(X))2=((b-a)^2)/12,
среднее квадратическое отклонение ?(Х)=?D(X)=(b-a)/(2?3).
Из условия задачи
?(Х)=?3·18=(b-a)/(2?3) ? b-a=6·18=108,
М(Х)=18=(a+b)/2 ? a+b=36.
Отсюда находим а=-36, b=72.
Следовательно, f(x)=1/108 при х?(-36, 72); f(x)=0 при х?(-36, 72)
Определим вероятность попадания Х в интервал (18, 36) по формуле
Р(c<X<d)=cd[$8747$]f(x)dx=(d-c)/(b-a).
Получим: Р(18<X<36)=(36-18)/108=1/6.
Плотность вероятности случайной величины Х, равномерно распределённой в интервале (a, b), задаётся следующим образом:
f(x)=1/(b-a) при х?(a, b); f(x)=0 при х?(a, b).
Её математическое ожидание М(Х)=ab[$8747$]хf(x)dx=(a+b)/2,
дисперсия D(X)=ab[$8747$]х2f(x)dx-(M(X))2=((b-a)^2)/12,
среднее квадратическое отклонение ?(Х)=?D(X)=(b-a)/(2?3).
Из условия задачи
?(Х)=?3·18=(b-a)/(2?3) ? b-a=6·18=108,
М(Х)=18=(a+b)/2 ? a+b=36.
Отсюда находим а=-36, b=72.
Следовательно, f(x)=1/108 при х?(-36, 72); f(x)=0 при х?(-36, 72)
Определим вероятность попадания Х в интервал (18, 36) по формуле
Р(c<X<d)=cd[$8747$]f(x)dx=(d-c)/(b-a).
Получим: Р(18<X<36)=(36-18)/108=1/6.
5
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