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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Независимые случайные величины X и Y заданы законами распределения. Составить законы распределения: а) произведения, б) суммы. Проверить свойство M(X+Y)=M(X)+M(Y).
Независимые случайные величины X и Y заданы законами распределения. Составить законы распределения: а) произведения, б) суммы.
Составить закон распределения дискретной случайной величины -- значит перечислить все её возможные значения и вычислить вероятности, с которыми она эти значения принимает.
а) Значения случайной величины получаются путём умножения всех возможных попарных комбинаций значений случайных величин и Эти значения таковы:
Поскольку только тогда, когда постольку по теореме умножения вероятностей независимых событий
Аналогично
При этом условие нормировки выполняется:
Таким образом, искомый закон распределения случайной величины можно задать в виде следующего ряда распределения:
б) Значения случайной величины получаются путём сложения всех возможных попарных комбинаций значений случайных величин и . Эти значения таковы:
Все значения различны. Поэтому
При этом условие нормировки выполняется:
Таким образом, искомый закон распределения случайной величины можно задать в виде следующего ряда распределения:
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peach2000 
получаются путём умножения всех возможных попарных комбинаций значений случайных величин 
и 
Эти значения таковы:
только тогда, когда 
постольку по теореме умножения вероятностей независимых событий
получаются путём сложения всех возможных попарных комбинаций значений случайных величин 
. Эти значения таковы:
Все значения 
