名校
1 . 在概率统计中,常常用频率估计概率.已知袋中有若干个红球和白球,有放回地随机摸球
次,红球出现
次.假设每次摸出红球的概率为
,根据频率估计概率的思想,则每次摸出红球的概率
的估计值为
.
(1)若袋中这两种颜色球的个数之比为
,不知道哪种颜色的球多.有放回地随机摸取3个球,设摸出的球为红球的次数为
,则
.
(注:
表示当每次摸出红球的概率为
时,摸出红球次数为
的概率)
(ⅰ)完成下表,并写出计算过程;
(ⅱ)在统计理论中,把使得
的取值达到最大时的
,作为
的估计值,记为
,请写出
的值.
(2)把(1)中“使得
的取值达到最大时的
作为
的估计值
”的思想称为最大似然原理.基于最大似然原理的最大似然参数估计方法称为最大似然估计.具体步骤:先对参数
构建对数似然函数
,再对其关于参数
求导,得到似然方程
,最后求解参数
的估计值.已知
的参数
的对数似然函数为
,其中
.求参数
的估计值,并且说明频率估计概率的合理性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/613f6de938db4bb3a7f98226d3a4c793.png)
(1)若袋中这两种颜色球的个数之比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5881f1ce9b4172ca346032d0fd1e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fadbd1d2d0294d04834dde31e0e4caaf.png)
(注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c74de541a96a252ca6b4bf05381a03ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(ⅰ)完成下表,并写出计算过程;
0 | 1 | 2 | 3 | |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c74de541a96a252ca6b4bf05381a03ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf2e58249dd993ae42a7bd6d9ba0005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf2e58249dd993ae42a7bd6d9ba0005.png)
(2)把(1)中“使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c74de541a96a252ca6b4bf05381a03ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf2e58249dd993ae42a7bd6d9ba0005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0807dbbfdeeaeffd987c4de037b892f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb13cf58c2aa7591391cfa8d515dc64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1aecbef5ad07da9949972dbcb9d659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c21d19789d426d0ed871d45ac6175f66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889b80977780bb8caec3c90954b91a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
7日内更新
|
199次组卷
|
7卷引用:重庆市七校联盟2024届高三下学期三诊考试数学试题
重庆市七校联盟2024届高三下学期三诊考试数学试题浙江省杭州市2024届高三下学期4月教学质量检测数学试题吉林省长春市实验中学2024届高三下学期对位演练考试数学试卷(一)(已下线)压轴题08计数原理、二项式定理、概率统计压轴题6题型汇总贵州省贵阳市第一中学等校2024届高三下学期三模数学试题山东省青岛第一中学2023-2024学年高二下学期第一次模块考试数学试题(已下线)专题02 高二下期末真题精选(压轴题 )-高二期末考点大串讲(人教A版2019)
名校
解题方法
2 . 已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beff0aabd2bb1fe031b658c55258ece8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db30ad779d5ff572a140cd6e3b0d3c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d75280bf1f91ea4d4d806d604d36977.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-06-14更新
|
627次组卷
|
4卷引用:重庆市重庆乌江新高考协作体2024届高三下学期模拟监测(三)数学试题
名校
3 . 已知函数
的图象在
处的切线过点
.
(1)求
在
上的最小值;
(2)判断
在
内零点的个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c658fcc638032c851f306a7344633a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cf818dd484cc4cebd40a5f28eb8e9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230b59c53740bcdd3ceca2cd9f860a7b.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aecfa6fa4f19b36faec90efba4fe2f7.png)
您最近一年使用:0次
2024-06-10更新
|
627次组卷
|
4卷引用:重庆市开州中学2023-2024学年高三下学期高考模拟考试数学试题(四)
名校
解题方法
4 . 已知直线
与函数
的图象相切(
),则
(e为自然对数的底数)的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d401abc3ec6537dfdc4e88fd195f521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fba64ec90d6532ff556660abfcfbcb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0767ea80b0700e2dbd3f1874cdae3a9b.png)
A.0 | B.1 | C.2 | D.e |
您最近一年使用:0次
2024-06-08更新
|
565次组卷
|
2卷引用:重庆市第一中学校2024届高三下学期5月月考测试数学试题
名校
解题方法
5 . 如图,将一块边长为4m的正方形铁片上有四块阴影部分,将这些阴影部分裁下来,然后用余下的四个全等的等腰三角形加工成一个正四棱锥形容器,下列说法正确的是( )
A.当![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() |
D.正四棱锥的体积最大值为![]() |
您最近一年使用:0次
2024-05-28更新
|
394次组卷
|
2卷引用:重庆市重庆乌江新高考协作体2024届高三下学期模拟监测(三)数学试题
名校
解题方法
6 . 与曲线在某点处的切线垂直,且过该点的直线称为曲线在某点处的法线,则曲线
的法线的纵截距的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c904567c3b3734e1eca8d042ef7a7b2d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
7 . 函数极限是现代数学中非常重要的概念,函数
在
处的极限定义如下:
,存在正数
,当
时,均有
,则称
在
处的极限为A,记为
,例如:
在
处的极限为2,理由是:
,存在正数
,当
时,均有
,所以
.已知函数
,
,(
,
为自然对数的底数).
(1)证明:
在
处的极限为
;
(2)若
,
,
,求
的最大值;
(3)若
,用函数极限的定义证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c9705e4d8649224c47228f0d1d0f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700458c01a7ad031e27d80ed43e9e882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09806564a0244b420341e5366f136f58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761be12e359f89c7627eb9200ba0912b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8abb00b0020eb89f4d18d1a5903f8a32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3cc66b811ad2395efe04d93b61c711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c9705e4d8649224c47228f0d1d0f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08c75767ddbba7462a85c9061334f3ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b55b95a7e906eeab34824633ddcae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c905859cee13de51b09fa4ed56bcfb25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67a4f8bfae051fca5537eca72aff172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1381493282b0864315ac49f14eeca20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94f94e5acf49264b65ad8bc4b92d316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187c21027ff08411931d32c530b64fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd1d338bd463d522aafd98357c4c012.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a9bb26472ca40b8a619bfd9ea06a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2492d486aef92677bc4d9c88c28b6845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90132e65026968c74776c719242ecd0c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b85c1784366cf7f60aa01dd62e529d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c58fea3170ce3e4fabed81babd54de1.png)
您最近一年使用:0次
解题方法
8 . 已知椭圆
的左、右焦点分别为
,点
是其左、右顶点,点
为
上异于
的点,满足直线
与
的斜率之积为
的周长为6.
(1)求椭圆
的方程;
(2)直线
过点
,与椭圆
交于
两点,当
外接圆面积最小时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a924529d8ab2815a8a9bd58ff366cf.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bc453cb750bc9b348fc682033feebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
9 . 若关于
的方程
有解,则实数m的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae9afe440a17a3898846656107fedd2.png)
您最近一年使用:0次
2024-05-16更新
|
1217次组卷
|
5卷引用:重庆市乌江新高考协作体2024届高考模拟监测(二)数学试题
名校
解题方法
10 . 设函数
,
,若存在
,
,使得
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8867b600581522ab45b638ad029c3ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2b18941336b298701ca66f3388a01e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
A.![]() | B.1 | C.2 | D.![]() |
您最近一年使用:0次
2024-04-26更新
|
3193次组卷
|
7卷引用:重庆市重庆乌江新高考协作体2024届高三下学期模拟监测(三)数学试题