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Консультация № 199598
13.11.2020, 18:38
0.00 руб.
14.11.2020, 14:21
1
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Независимые случайные величины Х и У заданы следующими зако-
нами:
Составьте законы распределения случайных величин Х+У и Х-У и най-
дите их математическое ожидание и дисперсию.
Независимые случайные величины Х и У заданы следующими зако-
нами:
Составьте законы распределения случайных величин Х+У и Х-У и най-
дите их математическое ожидание и дисперсию.
Прикрепленные файлы:
Обсуждение
18.11.2020, 05:28
общий
это ответ
Здравствуйте, anton_grigorov!
Для двух независимых случайных величин X и Y принимающих соответственно значения x[sub]1[/sub], x[sub]2[/sub],... x[sub]m[/sub] с вероятностью p[sub]x1[/sub], p[sub]x2[/sub],... p[sub]xm[/sub] и значения y[sub]1[/sub], y[sub]2[/sub],... y[sub]n[/sub] с вероятностью p[sub]y1[/sub], p[sub]y2[/sub],... p[sub]yn[/sub], имеем
В данном случае
то есть случайная величина X+Y будет распределена по закону:
(для контроля можно найти сумму всех вероятностей - она равна 1).
Основные моменты дискретной случайной величины определяются по формулам:
В данном случае
Для проверки можно найти моменты исходных случайных величин:
и воспользоваться свойствами моментов некоррелированных случайных величин:
Аналогично, для X-Y имеем
и закон распределения:
откуда
либо (по тем же свойствам)
Для двух независимых случайных величин X и Y принимающих соответственно значения x[sub]1[/sub], x[sub]2[/sub],... x[sub]m[/sub] с вероятностью p[sub]x1[/sub], p[sub]x2[/sub],... p[sub]xm[/sub] и значения y[sub]1[/sub], y[sub]2[/sub],... y[sub]n[/sub] с вероятностью p[sub]y1[/sub], p[sub]y2[/sub],... p[sub]yn[/sub], имеем
В данном случае
то есть случайная величина X+Y будет распределена по закону:
(для контроля можно найти сумму всех вероятностей - она равна 1).
Основные моменты дискретной случайной величины определяются по формулам:
В данном случае
Для проверки можно найти моменты исходных случайных величин:
и воспользоваться свойствами моментов некоррелированных случайных величин:
Аналогично, для X-Y имеем
и закон распределения:
откуда
либо (по тем же свойствам)
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