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Консультация № 196810
25.10.2019, 15:45
0.00 руб.
25.10.2019, 18:58
0
4
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Для случайной величины X, распределенной по нормальному закону, известны математическое ожидание M(X) и дисперсия D(X). Записать плотность вероятности f(x) и найти вероятность попадания случайной величины X в интервал (,):
M(X) = 8, D(X) = 4, (5,10);
Для случайной величины X, распределенной по нормальному закону, известны математическое ожидание M(X) и дисперсия D(X). Записать плотность вероятности f(x) и найти вероятность попадания случайной величины X в интервал (,):
M(X) = 8, D(X) = 4, (5,10);
Обсуждение
30.10.2019, 15:27
общий
это ответ
Здравствуйте, Женя!
Плотность вероятности случайной величины X, распределённой по нормальному закону с математическим ожиданием MX и дисперсией DX, определяется выражением
В данном случае MX = 8, DX = 4 и
Вероятность попадания любой непрерывной случайной величины X в интервал (a, b) определяется выражением
где F - функция распределения случайной величины X. Для нормального распределения её можно вычислить по формуле
где [$934$] - функция стандартного нормального распределения, обычно определяемая по таблице. В данном случае a = 5, b = 10 и
Плотность вероятности случайной величины X, распределённой по нормальному закону с математическим ожиданием MX и дисперсией DX, определяется выражением
В данном случае MX = 8, DX = 4 и
Вероятность попадания любой непрерывной случайной величины X в интервал (a, b) определяется выражением
где F - функция распределения случайной величины X. Для нормального распределения её можно вычислить по формуле
где [$934$] - функция стандартного нормального распределения, обычно определяемая по таблице. В данном случае a = 5, b = 10 и
5
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