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Здравствуйте! У меня возникли сложности с таким вопросом:
Случайная величина Х задана интегральной функцией распределения F (x) . 1) найти коэффициент А 2) найти дифференциальную функцию f (x) (плотность вероятности). 3) найти математическое ожидание и дисперсию 4) постройте график интегральной и дифференциальной функции 0, х≤0; F (x) = {Ах², 0<х≤5; 1, х>5.
Прежде чем приступить к решению задачи, я хочу поинтересоваться у Вас: "Вы прочитали в учебнике нужный теоретический материал?" Мне не хочется помимо решения задачи излагать ещё и теорию.
Вы понимаете, о чём я у Вас спрашиваю? Если понимаете, то почему не отвечаете на мой вопрос? Задача, записанная Вами, лёгкая. Разумеется, для тех, кто прочитал теорию и усвоил её. Поэтому мне не совсем понятно, что Вы имеете в виду, когда пишете: Цитата: Elena
Поскольку Вы гордо молчите в ответ на мои сообщения, постольку я могу написать Вам следующее.
Пусть случайная величина задана интегральной функцией распределения
Исходя из условия непрерывности функции в точке получим
Дифференцируя выражение для при получим
Тогда
Остаётся только построить графики функций и по известным, указанным выше выражениям. С этим Вы справитесь самостоятельно - задача для школьника. Предварительно проверьте, пожалуйста, мои расчёты во избежание ошибок.
Конечно, если у Вас возникнут вопросы, то задавайте их в мини-форуме консультации. На вопросы, связанные с теорией, постарайтесь найти ответы в учебнике. Я буду отвечать только на те вопросы, которые непосредственно связаны с расчётами в предложенном выше решении.
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Elena 
задана интегральной функцией распределения
в точке 
получим
получим
по известным, указанным выше выражениям. С этим Вы справитесь самостоятельно - задача для школьника. Предварительно проверьте, пожалуйста, мои расчёты во избежание ошибок. 
