问题
解答题
为缓解某路段交通压力,计划将该路段实施“交通限行”.在该路段随机抽查了50人,了解公众对“该路段限行”的态度,将调查情况进行整理,制成下表:
(2)若从年龄在[15,25),[25,35)的被调查者中各随机选取两人进行追踪调查,记选中的4人中不赞成“交通限行”的人数为ξ,求随机变量ξ的分布列和数学期望. |
答案
(1)如图
(2) ξ的分布列是
| ξ | 0 | 1 | 2 | 3 |
| P |  |  |  |  |
(1)各组的频率分别是0.1,0.2,0.3,0.2,0.1,0.1.
所以图中各组的纵坐标分别是:0.01,0.02,0.03,0.02,0.01,0.01.
则频率分布直方图如图.
(2)ξ所有可能取值有0,1,2,3,
P(ξ=0)=
·
=
×
=
.
P(ξ=1)=
×+×
=
×+×
=
.
P(ξ=2)=
×+×
=×+×
=
.
P(ξ=3)=·=×=
.
所以ξ的分布列是
| ξ | 0 | 1 | 2 | 3 |
| P | | | | |
+
+
=.