名校
解题方法
1 . 已知向量
,函数
.
(1)当
时,求
的单调递增区间;
(2)将
的图象向左平移
个单位长度后,所得图象对应的函数为
,若关于
的方程
在
上恰有两个不相等的实根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2500c8a420649ae5b6f370766e2f9d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/737fead0e09a10e7f24977a70644d1a6.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d75408bc3e0a180edd4960d1a3e2330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5c07fdcc3b6ce18e72bc873c624f1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2 . 已知椭圆
的离心率为
,且过点
.过椭圆
上的点
作圆
的两条切线,其中一条切线与椭圆
相交于点
,与圆
相切于点
,两条切线与
轴分别交于
两点.
的方程;
(2)
是否为定值,若是,请求出
的值;若不是,请说明理由:
(3)若椭圆上点
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90627d25fa0d0e5345c834b96331e77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959e5ab675f526dfb54b05f8f82151b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2228629b80d4efbfd2a226a863274520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2228629b80d4efbfd2a226a863274520.png)
(3)若椭圆上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c81a4d934b8e4565969a8e7921111c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
您最近一年使用:0次
3 . “南澳牡蛎”是我国地理标志产品,产量高、肉质肥、营养好,素有“海洋牛奶精品”的美誉.2024年该基地考虑增加人工投入,现有以往的人工投入增量x(人)与年收益增量y(万元)的数据如下:
该基地为了预测人工投入增量为16人时的年收益增量,建立了y与x的两个回归模型:
模型①:由最小二乘公式可求得y与x的线性回归方程:
;
模型②:由散点图的样本点分布,可以认为样本点集中在曲线:
的附近,对人工投入增量x做变换,令
,则
,且有
,
,
,
.
(ii)根据下列表格中的数据,比较两种模型的决定系数
,并选择拟合精度更高、更可靠的模型,预测人工投入增量为16人时的年收益增量.
(2)根据养殖规模与以往的养殖经验,产自某南澳牡蛎养殖基地的单个“南澳牡蛎”质量(克)在正常环境下服从正态分布
.购买10只该基地的“南澳牡蛎”,会买到质量小于20g的牡蛎的可能性有多大?
附:若随机变量
,则
,
;
样本
的最小二乘估计公式为:
,
,
.
人工投入增量x(人) | 2 | 3 | 4 | 6 | 8 | 10 | 13 |
年收益增量y(万元) | 13 | 22 | 31 | 42 | 50 | 56 | 58 |
模型①:由最小二乘公式可求得y与x的线性回归方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bc4486ffeb321242a9982309efff8c.png)
模型②:由散点图的样本点分布,可以认为样本点集中在曲线:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b328c19977481e5ea0ca585af1ef4394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b90ca3b73b0040365d9f55be51433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8ee45ed2358f5d5ad60eaf4c8830da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3af5d6a45c01b7d0c7c537506e1c56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c4fac1fe3facd6cec349abafe3ae59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1aec923d21f9cdf93c257769eca972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79728a92965ea4df0a12de9878245297.png)
(ii)根据下列表格中的数据,比较两种模型的决定系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
回归模型 | 模型① | 模型② |
回归方程 | ![]() | ![]() |
![]() | 182.4 | 79.2 |
(2)根据养殖规模与以往的养殖经验,产自某南澳牡蛎养殖基地的单个“南澳牡蛎”质量(克)在正常环境下服从正态分布
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b855415af8163cef49c0706e3c0528b.png)
附:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e188b5f28f5dc86364cb18c11f8d4702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c741455594dbc5293c436d8d2c0275.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eabdfcbc03a1d0b223555af8dbf4315.png)
样本
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539241dbd325e8aef033e0a89ff60125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853e9ba2d135b2d324679c0f4110149a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebff20f21ae41fd8d1f1e3145895842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f763c9590d5ca681acf466e4c6d7fa2.png)
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4 . 某高中学校有室内、室外两个运动场.假设同学们可以任意选择其中一个运动场锻炼,也可选择不锻炼,一天最多锻炼一次,一次只能选择一个运动场.若同学们每次锻炼选择去室内、室外运动场的概率均为0.5,每次选择相互独立.设
同学三天内去运动场锻炼的次数为
,已知
的分布列如下:(其中
)
(1)记事件
表示
同学三天内去运动场锻炼
次
;事件
表示
同学在这三天内去室内运动场锻炼的次数大于去室外运动场锻炼的次数.当
时,试根据全概率公式求
的值;
(2)是否存在实数
,使得
?若存在,求
的值;若不存在,请说明理由;
(3)记
表示事件“室外运动场举办集体锻炼活动”,
表示事件“王同学去室外运动场锻炼”,
.已知
同学在室外运动场举办集体锻炼活动的情况下去室外运动场锻炼的概率,比不举办集体锻炼活动的情况下去室外运动场锻炼的概率大,试比较
与
的大小,并证明之.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e362ab25e6f8719efd1b515094b69561.png)
![]() | 0 | 1 | 2 | 3 |
![]() | ![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eef5855dd54b607a61027e0b212cd61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108ab49f370919e730e3567070deee65.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667df0f959f5626681d6d9aecaf05be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efafab9402e42c2212489d7b9408c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697e2bfec979c21b2ba96569f82dba64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519abef903d663a9633f5ac89bc45fe0.png)
您最近一年使用:0次
解题方法
5 . 在平面直角坐标系
中,已知动点
到定点
的距离和它到定直线
的距离之比为
,记
的轨迹为曲线
.
(1)求
的方程;
(2)已知点
,不过
的直线
与
交于
,
两点,直线
,
,
的斜率依次成等比数列,求
到
距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ce47fde921058026708a4321a0e213.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e9efa96b6ec20a6ce18c7f458e4379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
6 . 某射击运动员进行射击训练,已知其每次命中目标的概率均为
.
(1)若该运动员共射击6次,求其在恰好命中3次的条件下,第3次没有命中的概率;
(2)该运动员射击训练不超过n(
)次,当他命中两次时停止射击(射击n次后,若命中的次数不足两次也不再继续),设随机变量X为该运动员的射击次数,试写出随机变量X的分布列,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)若该运动员共射击6次,求其在恰好命中3次的条件下,第3次没有命中的概率;
(2)该运动员射击训练不超过n(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ab800bb4666f21dbe05ec239ca39ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f0d793fc77a1befa103b46f0d5307b.png)
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7 . 已知两条抛物线
,
.
(1)求
与
在第一象限的交点的坐标.
(2)已知点A,B,C都在曲线
上,直线AB和AC均与
相切.
(ⅰ)求证:直线BC也与
相切.
(ⅱ)设直线AB,AC,BC分别与曲线
相切于D,E,F三点,记
的面积为
,
的面积为
.试判断
是否为定值,若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8a3bffe545af2299cf999d44767206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1138c04fc3a0e1c217db0d432e4aff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知点A,B,C都在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(ⅰ)求证:直线BC也与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(ⅱ)设直线AB,AC,BC分别与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
名校
解题方法
8 . 已知某系统由一个电源和并联的
三个元件组成,在电源电压正常的情况下,至少一个元件正常工作才可保证系统正常运行,电源及各元件之间工作相互独立.
(1)电源电压
(单位:
)服从正态分布
,且
的累积分布函数为
,求
.
(2)在统计中,指数分布常用于描述事件发生的时间间隔.已知随机变量
(单位:天)表示某元件的使用寿命,
服从指数分布,其累积分布函数为
.
(ⅰ)设
,证明:
;
(ⅱ)若第
天只有元件
发生故障,求第
天系统正常运行的条件概率.
附:若随机变量
服从正态分布
,则
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
(1)电源电压
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/515c70580e9f247fe27b2f0c964bc5ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166b72040b0aa1e70564fa174b91f6b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb8c83d6dd000e7c0180d91ed146a90.png)
(2)在统计中,指数分布常用于描述事件发生的时间间隔.已知随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d377090d1f35e2b0f2061052e238a8.png)
(ⅰ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f9a9793d0ce6ccb20dc7972d59e73f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7ac9cc03bbbb308beaa88f424fc1dc.png)
(ⅱ)若第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
附:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f77553716bd8b2f4680893d6d496b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd61d3462563f0964a9fde5537eaef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42373c7a83e1e876aa12d7e6ac028a17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28613181e6953c9858da252bfd62c569.png)
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解题方法
9 . 密码锁是锁的一种,开启时用的是一系列的数字或符号,文字密码锁可分为机械密码锁、数字密码锁等.现有一数字密码锁试验.
(1)若该密码锁的密码有三位,每位由数字
随机设置,现随机选择一个密码进行开锁试验,求开锁成功的概率;
(2)为了增加试验的趣味性,设置A,B,C,D四个互不相同的密码,每次使用其中一个且每次从上一次未使用的密码中随机选择一个,若第一次使用A密码,记第
次使用
密码的概率为
.
(i)求
;
(ii)设前
次试验中使用
密码的次数为
,求
.
(1)若该密码锁的密码有三位,每位由数字
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03433c4e7c0bdc696bcce5033498a759.png)
(2)为了增加试验的趣味性,设置A,B,C,D四个互不相同的密码,每次使用其中一个且每次从上一次未使用的密码中随机选择一个,若第一次使用A密码,记第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
(ii)设前
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
您最近一年使用:0次
名校
10 . 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)
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7卷引用: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
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