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Консультация № 196808
25.10.2019, 15:34
0.00 руб.
25.10.2019, 19:01
0
3
1
Здравствуйте! У меня возникли сложности с таким вопросом:
У охотника 4 патрона. Он стреляет по зайцу, пока не попадет или пока не кончаться патроны. Найдите математическое ожидание количества выстрелов, если вероятность попадания при одном выстреле 0,25.
У охотника 4 патрона. Он стреляет по зайцу, пока не попадет или пока не кончаться патроны. Найдите математическое ожидание количества выстрелов, если вероятность попадания при одном выстреле 0,25.
Обсуждение
30.10.2019, 14:50
общий
это ответ
Здравствуйте, Женя!
Пусть p = 0.25 - вероятность попадания при одном выстреле, тогда q = 1 - p = 0.75 - вероятность промаха при одном выстреле, и вероятность попадания с n-го выстрела будет равна pq[sup]n-1[/sup]. Следовательно, требуется найти математическое ожидание дискретной случайной величины X (количество выстрелов), принимающей значения x[sub]1[/sub] = 1, x[sub]2[/sub] = 2, x[sub]3[/sub] = 3, x[sub]4[/sub] = 4 с вероятностью
(последняя величина есть сумма вероятностей двух событий - "попадание с четвёртого выстрела" и "четыре промаха"). Математическое ожидание такой случайной величины определяется по формуле:
или в данном случае
Пусть p = 0.25 - вероятность попадания при одном выстреле, тогда q = 1 - p = 0.75 - вероятность промаха при одном выстреле, и вероятность попадания с n-го выстрела будет равна pq[sup]n-1[/sup]. Следовательно, требуется найти математическое ожидание дискретной случайной величины X (количество выстрелов), принимающей значения x[sub]1[/sub] = 1, x[sub]2[/sub] = 2, x[sub]3[/sub] = 3, x[sub]4[/sub] = 4 с вероятностью
(последняя величина есть сумма вероятностей двух событий - "попадание с четвёртого выстрела" и "четыре промаха"). Математическое ожидание такой случайной величины определяется по формуле:
или в данном случае
5
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