题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014538-65109.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014538-80349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014539-34870.gif)
(I)求他们选择的车床类型互不相同的概率;
(II)设ξ为他们选择甲型或丙型车床的人数,求ξ的分布列及数学期望.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014539-68939.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014539-27097.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014539-27097.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014539-96750.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014540-96200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014540-75198.gif)
由题意知
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014540-31832.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014540-62914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014540-35944.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014541-18007.gif)
相互独立且
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014541-67709.gif)
(1)他们选择的车床类型互不相同的概率为
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014541-13254.gif)
(2)解法1:设3名工人中选择乙型车床的人数为
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014542-34475.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014542-31976.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014542-26316.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014542-41394.gif)
ξ | 0 | 1 | 2 | 3 |
P | ![]() | ![]() | ![]() | ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014539-27097.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014539-27097.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014539-96750.gif)
解法2:设第
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014540-96200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014544-75715.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014544-27356.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014544-14664.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014544-62883.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014545-99180.gif)
分布列同法1,
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030014545-81011.gif)
核心考点
试题【某大型工厂的车床有甲,乙,丙三个型号,分别占总数的,,,现在有三名工人各自独立选一台车床操作.(I)求他们选择的车床类型互不相同的概率;(II)设ξ为他们选择甲】;主要考察你对离散型随机变量均值与方差等知识点的理解。[详细]
举一反三