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Консультация № 190674
09.03.2017, 03:01
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Здравствуйте! У меня возникли сложности с таким вопросом:
Нормально распределенная случайная величина имеет следующую функцию распределения: F(x) = 0,5 + 0,5Ф(x-1). Из какого интервала (1;2) или (2;6) она примет значение с большей вероятностью?
Нормально распределенная случайная величина имеет следующую функцию распределения: F(x) = 0,5 + 0,5Ф(x-1). Из какого интервала (1;2) или (2;6) она примет значение с большей вероятностью?
Обсуждение
09.03.2017, 05:50
общий
это ответ
Здравствуйте, katysha.egorova!
Вероятность того, что случайная величина с функцией распределения F(x) примет значение из интервала (a;b) равна
В данном случае F(x) = 0.5 + 0.5[$934$](x-1), поэтому
Значения функции стандартного нормального распределения [$934$](x) берём из таблицы: [$934$](0) = 0.5, [$934$](1) = 0.84135, [$934$](5) = 0.99999. Тогда
то есть случайная величина с большей вероятностью примет значение из интервала (1;2).
Вероятность того, что случайная величина с функцией распределения F(x) примет значение из интервала (a;b) равна
В данном случае F(x) = 0.5 + 0.5[$934$](x-1), поэтому
Значения функции стандартного нормального распределения [$934$](x) берём из таблицы: [$934$](0) = 0.5, [$934$](1) = 0.84135, [$934$](5) = 0.99999. Тогда
то есть случайная величина с большей вероятностью примет значение из интервала (1;2).
5
Спасибо большое!<br>Вы молодец!
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