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06离散型随机变量的均值.pdf

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1、1/15 2 3 离散型随机变量的均值与方差231 离散型随机变量的均值教学目标：知识与技能：了解离散型随机变量的均值或期望的意义，会根据离散型随机变量的分布列求出均值或期望过程与方法：理解公式“Ea+b）=aE+b”，以及“若 Bn,p），则 E=np”.能熟练地应用它们求相应的离散型随机变量的均值或期望。情感、态度与价值观：承前启后，感悟数学与生活的和谐之美,体现数学的文化功能与人文价值。教学重点：离散型随机变量的均值或期望的概念教学难点：根据离散型随机变量的分布列求出均值或期望授课类型：新授课课时安排：4 课时教具：多媒体、实物投影仪教学过程：一、复习引入：1.随机变

2、量：如果随机实验的结果可以用一个变量来表示，那么这样的变量叫做随机变量随机变量常用希腊字母、等表示8jGSC5ZkyQ 2.离散型随机变量:对于随机变量可能取的值，可以按一定次序一一列出，这样的随机变量叫做离散型随机变量8jGSC5ZkyQ 2/15 3连续型随机变量:对于随机变量可能取的值，可以取某一区间内的一切值，这样的变量就叫做连续型随机变量8jGSC5ZkyQ 4.离散型随机变量与连续型随机变量的区别与联系:离散型随机变量与连续型随机变量都是用变量表示随机实验的结果；但是离散型随机变量的结果可以按一定次序一一列出，而连续性随机变量的结果不可以一一列出8jGSC5ZkyQ 若是随机变量，

3、baba,是常数，则也是随机变量并且不改变其属性离散型、连续型）5.分布列:设离散型随机变量可能取得值为x1，x2，,，x3，,，取每一个值xii=1，2，,）的概率为()iiPxp，则称表x1x2,xi,P P1P2,Pi,为随机变量的概率分布，简称的分布列6.分布列的两个性质：Pi0，i1，2，,；P1+P2+,=17.离散型随机变量的二项分布:在一次随机实验中，某事件可能发生也可能不发生，在n次独立重复实验中这个事件发生的次数是一个随机变量如果在一次实验中某事件发生的概率是P，那么在n次独立重复实验中这个事件恰好发生k次的概率是8jGSC5ZkyQ knkknnqpCkP)(，其

4、中n，p为参数，并记knkknqpCb(k；n，p8.离散型随机变量的几何分布：在独立重复实验中，某事件第一次发生时，所作实验的次数也是一个正整数的离散型随机变量“k”表示在第k 次独立重复实验时事件第一次发生.如果把 k 次实验时事件A 发生记为kA、事件A 不发生记为kA，P(kA=p，P(kA=q(q=1-p，那么8jGSC5ZkyQ 112311231()()()()()()()kkkkkPkP A A AAAP A P A P AP AP Aqp=1kqp，其中k0,1,2,，pq1二、讲解新课：根据已知随机变量的分布列，我们可以方便的得出随机变量的某些制定的概率，但分布列的用途远不

5、止于此，例如：已知某射手射击所得环数的分布列如下8jGSC5ZkyQ 4 5 6 7 8 9 10 P 0.02 0.04 0.06 0.09 0.28 0.29 0.22 在 n 次射击之前，可以根据这个分布列估计n 次射击的平均环数这就是我们今天要学习的离散型随机变量的均值或期望8jGSC5ZkyQ 根据射手射击所得环数的分布列，我们可以估计，在n 次射击中，预计大约有文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G

6、2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4

7、S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10

8、T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H

9、1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2

10、X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H

11、10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ

12、4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R34/15 nnP02.0)4(次得 4 环；nnP04.0)5(次得 5 环；,nnP22.0)10(次得 10 环故在 n 次射击的总环数大约为n02.04n04.05n22.01002.04(04.05n)22.010，从而，预计 n 次射击的平均环数约为02.0404.0532.822.010这是一个由射手射击所得环数的分布列得到的，只与射击环数的可能取值及其相应的概率有关的常数，它反映了射手射击的平均水平8jGSC5ZkyQ 对于任一射手

13、，若已知其射击所得环数的分布列，即已知各个)(iP，是随机变量，则也是随机变量，它们的分布列为x1x2,xn,bax1bax2,baxn,P p1p2,pn,于是E11)(pbax22)(pbax,nnpbax)(,11(pxa22px,nnpx,1(pb2p,np,baE，由此，我们得到了期望的一个性质:baEbaE)(5.若B，则Enp三、讲解范例：文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2

14、R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G

15、2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4

16、S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10

17、T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H

18、1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2

19、X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H

20、10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R36/15 例 1.篮球运动员在比赛中每次罚球命中得1 分，罚不中得0分，已知他命中的概率为0.7，求他罚球一次得分的期望8jGSC5ZkyQ 解：因为3.0)0(,7.0)1(PP，所以7.03.007.01E例 2.一次单元测验由20个选择题构成，每个选择题有4 个选项，其中有且仅有一个选项是正确答案，每题选择正确答案得5分，不作出选择或选错不得分，满分100分学生甲选对任一题的概率为 0.9，学生乙则在测验中对每题都从4 个选择中随机地选择一个，求学生甲和乙在这次英语单元测验中的成绩的期望8jG

21、SC5ZkyQ 解：设学生甲和乙在这次英语测验中正确答案的选择题个数分别是,，则 B+2 00000P(X2=2 000 8jGSC5ZkyQ=620000.01+2000(1-0.01=2 600,EX3=60000P(X3=60000+10 000 P(X3=10 000 +0 P(X3=0 8jGSC5ZkyQ=60 0000.01+100000.25=3100.采取方案 2 的平均损失最小，所以可以选择方案2.值得注意的是，上述结论是通过比较“平均损失”而得出的一般地，我们可以这样来理解“平均损失”：假设问题中的气文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H1

22、0T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4

23、H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E

24、2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9

25、H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:C

26、Q4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO

27、2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9

28、D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R38/15 象情况多次发生，那么采用方案2 将会使损失减到最小由于洪水是否发生以及洪水发生的大小都是随机的，所以对于个别的一次决策，采用方案 2 也不一定是最好的8jGSC5ZkyQ 例 4.随机抛掷一枚骰子，求所得骰子点数的期望解：6,2,1,6/1)(iiP，6/166/126/11E=3.5例 5.有一批数量很大的产品，其次品率是

29、15%，对这批产品进行抽查，每次抽取1 件，如果抽出次品，则抽查终止，否则继续抽查，直到抽出次品为止，但抽查次数不超过10 次求抽查次数的期望结果保留三个有效数字）8jGSC5ZkyQ 解：抽查次数取 110 的整数，从这批数量很大的产品中抽出 1 件检查的实验可以认为是彼此独立的，取出次品的概率是0.15，取出正品的概率是0.85，前1k次取出正品而第k次k=1，2，10）取出次品的概率：8jGSC5ZkyQ 15.085.0)(1kkP613.5抛掷骰子所得点数的数学期望，就是的所有可能取值的平均值例 7.某城市出租汽车的起步价为10 元，行驶路程不超出4km时租车费为10 元，若行驶路

30、程超出4km，则按每超出lkm 加收 2元计费(超出不足lkm 的部分按lkm 计从这个城市的民航机场到某宾馆的路程为15km某司机经常驾车在机场与此宾馆之间接送旅客，由于行车路线的不同以及途中停车时间要转换成行车路程(这个城市规定，每停车5 分钟按 lkm 路程计费，这个司机一次接送旅客的行车路程是一个随机变量设他所收租车费为8jGSC5ZkyQ(求租车费关于行车路程的关系式；(若随机变量的分布列为15161718P 0.10.50.30.1求所收租车费的数学期望(已知某旅客实付租车费38 元，而出租汽车实际行驶了15km，问出租车在途中因故停车累计最多几分钟?8jGSC5ZkyQ

31、解：(依题意得=2(-4 十 10，即=2+2；文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 Z

32、R9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档

33、编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W

34、1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7

35、 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3

36、文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U

37、3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R310/15(E4.161.0183.0175.0161.015=2+2 E2E+2=34.8 由 38=2+2，得 =18，5(18-15=15 所以出租车在途中因故停车累计最多15 分钟四、课堂练习：1.口袋中有

38、5 只球，编号为 1，2，3，4，5，从中任取 3 球，以表示取出球的最大号码，则E ）8jGSC5ZkyQ A4；B5；C4.5；D4.75答案：C2.篮球运动员在比赛中每次罚球命中的1 分，罚不中得0分已知某运动员罚球命中的概率为0.7，求他罚球 1 次的得分的数学期望；他罚球 2 次的得分的数学期望；他罚球 3 次的得分的数学期望解：因为7.0)1(P，3.0)0(P，所以E1)1(P07.0)0(P 的概率分布为0 1 2 P 23.03.07.012C27.0所以E009.0142.0298.01.4 的概率分布为文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9

39、D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码

40、:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1

41、HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 Z

42、R9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档

43、编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W

44、1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7

45、 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R311/15 2 3P 33.02133.07.0C3.07.0223C37.0所以E0027.01189.0298.02.1.3设有m升水，其中含有大肠杆菌n个今取水1 升进行化验，设其中含有大肠杆菌的个数为，求的数学期望8jGSC5ZkyQ 分析：任取1 升水，此升水中含一个大肠杆菌的概率是m1，事件“=k”发生，即n个大

46、肠杆菌中恰有k个在此升水中，由n次独立重复实验中事件A,进而可求E.8jGSC5ZkyQ 解：记事件A：“在所取的1 升水中含一个大肠杆菌”，则P(A=m1P(=k=Pn(k=Cknm1k(1 m1nk，故E=nm1=mn五、小结：(1 离散型随机变量的期望，反映了随机变量取值的平均水平；(2求离散型随机变量的期望的基本步骤：理解的意义，写出可能取的全部值；求取各个值的概率，写出分布列；根据分布列，由期望的定义求出E公式 Ea+b）=aE+b，以及服从二项分布的随机变量的期望E=np 8jGSC5ZkyQ 六、课后作业：P64-65练习 1,2,3,4 P69 A组 1,2,3 1.一袋

47、子里装有大小相同的3 个红球和两个黄球，从中同时取出 2 个，则其中含红球个数的数学期望是则的要布列为0 1 2 p 10353101于是 E=612924CC=1 时，取 1 黑 1 白 p(=1=31291314CCC=2 时，取 2 白或 1 红 1 黑 p(=2=2923CC+3611291412CCC=3 时，取 1 白 1 红，概率 p(=3=61291213CCC=4 时，取 2 红，概率 p(=4=3612922CC为分布列2）期望E=061+131+23611+361+4361=9143.学校新进了三台投影仪用于多媒体教学，为保证设备正常工作，0 1 2 3 4 p

48、6131361161361文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3

49、文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U

50、3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7V7 ZR9D9H10T2R3文档编码:CQ4H1G2U3W1 HO2E2X4S7

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关键词：: 06 离散随机变量均值

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