名校
1 . 第二次世界大战期间,了解德军坦克的生产能力对盟军具有非常重要的战略意义.已知德军的每辆坦克上都有一个按生产顺序从1开始的连续编号.假设德军某月生产的坦克总数为N,随机缴获该月生产的n辆(
)坦克的编号为
,
,…,
,记
,即缴获坦克中的最大编号.现考虑用概率统计的方法利用缴获的坦克编号信息估计总数N.
甲同学根据样本均值估计总体均值的思想,用
估计总体的均值,因此
,得
,故可用
作为N的估计.
乙同学对此提出异议,认为这种方法可能出现
的无意义结果.例如,当
,
时,若
,
,
,则
,此时
.
(1)当
,
时,求条件概率
;
(2)为了避免甲同学方法的缺点,乙同学提出直接用M作为N的估计值.当
,
时,求随机变量M的分布列和均值
;
(3)丙同学认为估计值的均值应稳定于实际值,但直观上可以发现
与N存在明确的大小关系,因此乙同学的方法也存在缺陷.请判断
与N的大小关系,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a5e1bb2637455d05313a112c5d745bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcf3400c1490071b390aaac0ad0e102.png)
甲同学根据样本均值估计总体均值的思想,用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb1694f46c040a6c976b2ef3eb3934b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120e4da3fe22be28b3bb28f28fbcc862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92da09d5877d3dfe1a856b6353b81906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7171e0c9c26b9f39a32d3a61d113cf.png)
乙同学对此提出异议,认为这种方法可能出现
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a1bd336033c63bc9c4f99ff2b482b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebcc133d5b11b33a904875182d8c8261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50a1cf3b1a6f9a12605cbdf48e5de5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49bf4a59874878184dadeec74d1781d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53722e8f43d44f9c611398ddaab151f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afac93e0089a7ffca9a1f720e13b6878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de3874d2e8c49308151837161d7aa91c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebcc133d5b11b33a904875182d8c8261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b9b7c101f267bbf233da7d3ac30e6f0.png)
(2)为了避免甲同学方法的缺点,乙同学提出直接用M作为N的估计值.当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270e5f2895909d5b6b6c612a8696565b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348388b2590255369527f86fd6be63c3.png)
(3)丙同学认为估计值的均值应稳定于实际值,但直观上可以发现
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348388b2590255369527f86fd6be63c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348388b2590255369527f86fd6be63c3.png)
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2024-06-11更新
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693次组卷
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3卷引用:广东省华南师范大学附属中学2024届高三下学期模拟测试(一)数学试题
名校
2 . 已知定义在
上的可导函数
满足
设
,则
的大小关系是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceec441fee8121b8b030438a518e521c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d140c889b03acddd985e7ab453711b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
A.![]() | B.![]() | C.![]() | D.![]() ![]() |
您最近一年使用:0次
2017-03-08更新
|
756次组卷
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3卷引用:【全国校级联考】广东省深圳实验,珠海一中等六校2019届高三第一次联考数学文试题