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Консультация № 194285
24.12.2018, 17:12
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Зона ответственности локатора определяется в полярных координатах неравенствами 0≤φ≤3π/4 и 10≤ρ≤100. В случайной точке зоны ответственности может появиться цель. Расстояние ее от локатора – случайная величина Х. Считая равновозможными все положения цели в зоне ответственности, найдите функцию распределения случайной величины Х и ее функцию плотности вероятности.
Зона ответственности локатора определяется в полярных координатах неравенствами 0≤φ≤3π/4 и 10≤ρ≤100. В случайной точке зоны ответственности может появиться цель. Расстояние ее от локатора – случайная величина Х. Считая равновозможными все положения цели в зоне ответственности, найдите функцию распределения случайной величины Х и ее функцию плотности вероятности.
Обсуждение
27.12.2018, 17:13
общий
это ответ
Здравствуйте, Анна Витальевна!
Известна следующая трактовка геометрической вероятности. Пусть плоская фигура
составляет часть плоской фигуры 
На фигуру 
наудачу брошена точка. Если предположить, что вероятность попадания брошенной точки на фигуру пропорциональна площади этой фигуры и не зависит ни от её расположения относительно 
ни от формы 
то вероятность попадания точки в фигуру определяется отношением площадей фигур и то есть
Кроме того, функцией
распределения случайной величины 
называют функцию, определяющую для каждого значения 
вероятность того, что случайная величина примет значение, меньшее 
то есть
Учитывая указанное выше и вид зоны ответственности локатора, принятой за фигуруполучим
Известна следующая трактовка геометрической вероятности. Пусть плоская фигура
составляет часть плоской фигуры На фигуру наудачу брошена точка. Если предположить, что вероятность попадания брошенной точки на фигуру пропорциональна площади этой фигуры и не зависит ни от её расположения относительно ни от формы то вероятность попадания точки в фигуру определяется отношением площадей фигур и то естьКроме того, функцией
распределения случайной величины называют функцию, определяющую для каждого значения вероятность того, что случайная величина примет значение, меньшее то естьУчитывая указанное выше и вид зоны ответственности локатора, принятой за фигуру
получим
Об авторе:
Facta loquuntur.
Facta loquuntur.
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