1 . 在数字
的任意一个排列
:
中,如果对于
,
,有
,那么就称
为一个逆序对.记排列
中逆序对的个数为
.如
时,在排列
:3,2,4,1中,逆序对有
,
,
,
,则
.
(1)设排列
:
,写出两组具体的排列
,分别满足:①
,②
;
(2)对于数字1,2,…,n的一切排列
,求所有
的算术平均值;
(3)如果把排列A:
中两个数字
交换位置,而其余数字的位置保持不变,那么就得到一个新的排列,
:
,求证:
为奇数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5929d3faf0bb567573cc46fabd30aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6d99dfbc36d9be71895dfdb732f321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f2c7c9305b404f7363a376af101aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ae1214cc78e72fb613d7e649bc27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a1d999ab14d86a73dd17df33f23b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bba7a40102e81f5759f7b05ebf5a18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990eaf5dbba84f199bdc438da81fcfa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0481d24e2af1e0cd348732b9444d1dde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ce2830528c2ea6b5d4df0c77644e33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b08a341f6e37e92710bf95531217e6.png)
(1)设排列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec99c57bf7997bd93e1ed8f48d5af9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42030a33382b003b81c2b148a216fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb79a2396402d62e725578f015e5c06a.png)
(2)对于数字1,2,…,n的一切排列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bba7a40102e81f5759f7b05ebf5a18c.png)
(3)如果把排列A:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e68f643eb061dea7def83952c1f56c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3d172f08313520e76b6cbc2ff9980c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c687695f558d18f8b220be874a723170.png)
您最近一年使用:0次
解题方法
2 . 为了拓展学生的知识面,提高学生对航空航天科技的兴趣,培养学生良好的科学素养,某校组织学生参加航空航天科普知识答题竞赛,每位参赛学生可答题若干次,答题赋分方法如下:第一次答题,答对得2分,答错得1分;从第二次答题开始,答对则获得上一次答题得分的两倍,答错得1分.学生甲参加这次答题竞赛,每次答对的概率为
,且每次答题结果互不影响.
(1)求学生甲前三次答题得分之和为4分的概率;
(2)设学生甲第
次答题所得分数
的数学期望为
.
(ⅰ)求
,
,
;
(ⅱ)写出
与
满足的等量关系式(直接写出结果,不必证明);
(ⅲ)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
(1)求学生甲前三次答题得分之和为4分的概率;
(2)设学生甲第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4c651746492cce239ee6bf113242ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56b678dec65a0ca8006cc6828d8cb501.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5e485d34d6b30c797bf58e90efb985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576074947c20baa9388a82b20d3bd4f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad58191cf84486be26a08508e192985e.png)
(ⅱ)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba8fe190e57f7b2a497c059ffb292dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7379bf07187d47913eb93a4e2f63926.png)
(ⅲ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675c24c622664ebf9bc3d6431ca7a75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
您最近一年使用:0次
2023-07-10更新
|
654次组卷
|
3卷引用:北京市通州区2022-2023学年高二下学期期末质量检测数学试题