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1 . 随着现代电子技术的迅猛发展,关于元件和系统可靠性的研究已发展成为一门新的学科——可靠性理论.在可靠性理论中,一个元件正常工作的概率称为该元件的可靠性.元件组成系统,系统正常工作的概率称为该系统的可靠性.现有
(
,
)种电子元件,每种2个,每个元件的可靠性均为
(
).当某元件不能正常工作时,该元件在电路中将形成断路.现要用这
个元件组成一个电路系统,有如下两种连接方案可供选择,当且仅当从A到B的电路为通路状态时,系统正常工作.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/7e8acff6-dd73-49e5-b7a2-13d3593082f8.png?resizew=393)
(1)(i)分别写出按方案①和方案②建立的电路系统的可靠性
、
(用
和
表示);
(ii)比较
与
的大小,说明哪种连接方案更稳定可靠;
(2)设
,
,已知按方案②建立的电路系统可以正常工作,记此时系统中损坏的元件个数为
,求随机变量
的分布列和数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c11f6c800b8e0410674a0c6d307d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/7e8acff6-dd73-49e5-b7a2-13d3593082f8.png?resizew=393)
(1)(i)分别写出按方案①和方案②建立的电路系统的可靠性
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(ii)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/949ab4f3efd2d63a97688c21098a7a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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2020-06-17更新
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2卷引用:吉林省东北师范大学附属中学2020届高三第四次模拟考试数学(理)试题