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人教版高中数学选修3离散型随机变量的方差教学设计
3.下结论.依据均值和方差做出结论.跟踪训练2. A、B两个投资项目的利润率分别为随机变量X1和X2，根据市场分析， X1和X2的分布列分别为X1 2% 8% 12% X2 5% 10%P 0.2 0.5 0.3 P 0.8 0.2求：(1)在A、B两个项目上各投资100万元， Y1和Y2分别表示投资项目A和B所获得的利润，求方差D(Y1)和D(Y2)；(2)根据得到的结论，对于投资者有什么建议？ 解：(1)题目可知，投资项目A和B所获得的利润Y1和Y2的分布列为：Y1 2 8 12 Y2 5 10P 0.2 0.5 0.3 P 0.8 0.2所以 ;; 解：(2) 由(1)可知 ，说明投资A项目比投资B项目期望收益要高；同时 ，说明投资A项目比投资B项目的实际收益相对于期望收益的平均波动要更大.因此，对于追求稳定的投资者，投资B项目更合适;而对于更看重利润并且愿意为了高利润承担风险的投资者，投资A项目更合适.
人教版高中数学选修3离散型随机变量的均值教学设计
对于离散型随机变量，可以由它的概率分布列确定与该随机变量相关事件的概率。但在实际问题中，有时我们更感兴趣的是随机变量的某些数字特征。例如，要了解某班同学在一次数学测验中的总体水平，很重要的是看平均分；要了解某班同学数学成绩是否“两极分化”则需要考察这个班数学成绩的方差。我们还常常希望直接通过数字来反映随机变量的某个方面的特征，最常用的有期望与方差.二、 探究新知探究1.甲乙两名射箭运动员射中目标靶的环数的分布列如下表所示：如何比较他们射箭水平的高低呢？环数X 7 8 9 10甲射中的概率 0.1 0.2 0.3 0.4乙射中的概率 0.15 0.25 0.4 0.2类似两组数据的比较,首先比较击中的平均环数,如果平均环数相等，再看稳定性.假设甲射箭n次，射中7环、8环、9环和10环的频率分别为：甲n次射箭射中的平均环数当n足够大时，频率稳定于概率，所以x稳定于7×0.1+8×0.2+9×0.3+10×0.4=9.即甲射中平均环数的稳定值(理论平均值)为9,这个平均值的大小可以反映甲运动员的射箭水平.同理，乙射中环数的平均值为7×0.15+8×0.25+9×0.4+10×0.2=8.65.
人教版高中数学选修3分类变量与列联表教学设计
一、 问题导学前面两节所讨论的变量,如人的身高、树的胸径、树的高度、短跑100m世界纪录和创纪录的时间等,都是数值变量,数值变量的取值为实数.其大小和运算都有实际含义.在现实生活中,人们经常需要回答一定范围内的两种现象或性质之间是否存在关联性或相互影响的问题.例如,就读不同学校是否对学生的成绩有影响,不同班级学生用于体育锻炼的时间是否有差别,吸烟是否会增加患肺癌的风险,等等,本节将要学习的独立性检验方法为我们提供了解决这类问题的方案。在讨论上述问题时,为了表述方便,我们经常会使用一种特殊的随机变量,以区别不同的现象或性质,这类随机变量称为分类变量.分类变量的取值可以用实数表示,例如,学生所在的班级可以用1,2,3等表示,男性、女性可以用1,0表示,等等.在很多时候,这些数值只作为编号使用,并没有通常的大小和运算意义,本节我们主要讨论取值于{0,1}的分类变量的关联性问题.
人教版高中数学选修3离散型随机变量及其分布列(2)教学设计
温故知新 1.离散型随机变量的定义可能取值为有限个或可以一一列举的随机变量,我们称为离散型随机变量.通常用大写英文字母表示随机变量,例如X,Y,Z;用小写英文字母表示随机变量的取值,例如x,y,z.随机变量的特点: 试验之前可以判断其可能出现的所有值，在试验之前不可能确定取何值；可以用数字表示2、随机变量的分类①离散型随机变量:X的取值可一、一列出；②连续型随机变量:X可以取某个区间内的一切值随机变量将随机事件的结果数量化．3、古典概型:①试验中所有可能出现的基本事件只有有限个；②每个基本事件出现的可能性相等。二、探究新知探究1.抛掷一枚骰子,所得的点数X有哪些值？取每个值的概率是多少？ 因为X取值范围是{1，2，3，4，5，6}而且"P(X=m)"=1/6,m=1,2,3,4,5,6.因此X分布列如下表所示
人教版高中数学选修3二项式系数的性质教学设计
1.对称性与首末两端“等距离”的两个二项式系数相等,即C_n^m=C_n^(n"-" m).2.增减性与最大值 当k(n+1)/2时,C_n^k随k的增加而减小.当n是偶数时,中间的一项C_n^(n/2)取得最大值;当n是奇数时,中间的两项C_n^((n"-" 1)/2) 与C_n^((n+1)/2)相等,且同时取得最大值.探究2.已知(1+x)^n =C_n^0+C_n^1 x+...〖+C〗_n^k x^k+...+C_n^n x^n 3.各二项式系数的和C_n^0+C_n^1+C_n^2+…+C_n^n=2n.令x=1 得(1+1)^n=C_n^0+C_n^1 +...+C_n^n=2^n所以，(a+b)^n 的展开式的各二项式系数之和为2^n1. 在(a+b)8的展开式中,二项式系数最大的项为 ,在(a+b)9的展开式中,二项式系数最大的项为 . 解析:因为(a+b)8的展开式中有9项,所以中间一项的二项式系数最大,该项为C_8^4a4b4=70a4b4.因为(a+b)9的展开式中有10项,所以中间两项的二项式系数最大,这两项分别为C_9^4a5b4=126a5b4,C_9^5a4b5=126a4b5.答案:1.70a4b4 126a5b4与126a4b5 2. A=C_n^0+C_n^2+C_n^4+…与B=C_n^1+C_n^3+C_n^5+…的大小关系是( )A.A>B B.A=B C.A<B D.不确定 解析:∵(1+1)n=C_n^0+C_n^1+C_n^2+…+C_n^n=2n,(1-1)n=C_n^0-C_n^1+C_n^2-…+(-1)nC_n^n=0,∴C_n^0+C_n^2+C_n^4+…=C_n^1+C_n^3+C_n^5+…=2n-1,即A=B.答案:B
2022年黑龙江省龙东地区中考英语真题（原卷版）
B: It’s about theexperiments three astronauts are doing on the space station.A: That’s great. I’minterested in space, so I want to be an astronaut like them.
2022年黑龙江省绥化市中考英语真题（解析版）
There are many kinds ___21___art forms in China. ___22___ you often see any of them in your life?They help us understand and enjoy the traditional Chinese culture. When theSpring Festival comes, some people often ___23___ the red paper intodifferent art works with scissors.
2022年黑龙江省大庆市中考英语试题（解析版）
On a snowy day, there was a man walking in ahurry on the road. His clothes were in poor condition. You might think he was abeggar（乞丐）,but in fact he was a painter. His name was Vincent Willem van Gogh.
2022年黑龙江省哈尔滨市中考英语真题（原卷版）
I often use old clothes that people don’t wearany more to make bags. I opened a small shop in my community and set up awebsite to sell the bags online. Many customers think they are fantastic. Now Iplan to write a new book about ways to use old clothes.
2022年辽宁省盘锦市中考英语真题（解析版）
Remember that it’s better to fail than it’s togive up, and the key is to learn from your failure(失败). But along withdifficulties, there will also be ____18____ wonderful waiting for you.
2022年江苏省宿迁市中考英语真题 （原卷版）
Theoil paper umbrella is a traditional Chinese handicraft（手工艺品）.It has a history of over 1,000 years in China．In early TangDynasty, it was introduced to Japan and Korea, so it was called the “TangUmbrella”. Later oil paper umbrellas were spread to other Asian countries, suchas Vietnam, Thailand and Laos, and each had its own style. However, assteel-ribbed（钢骨的）umbrellas appeared in the last century, thehand-made oil paper umbrellas became less used in daily life. They were turnedinto decorative artifacts（装饰性工艺品）.
2022年湖南省怀化市中考英语真题（原卷版）
___14___, I think an interest in Englishis very important. When I was in Grade Three, we had a new ___15___ — English,it was new for me. I was interested in it. I worked hard at it. Soon we had anEnglish exam and I got a very good mark. How ___16___ I was! After that,I learned English harder. Our English teacher often teaches us English songs,and ___17___ sound nice. I often think how interesting English is!
2022年湖南省常德市中考英语真题（解析版）
Bike-to-Work Day is held every year across North America on thethird Friday of May. It was started by the League of American Bicyclistsin 1956. Its aim is to promote (促进) the bicycle as a serious choice of getting toand from work. In today’s world where global warming is a serious issue, thebicycle is a perfect way of reducing our carbon (碳) footprint.
2022年湖北省鄂州市中考英语真题（原卷版）
Dealing with a nosebleed（鼻出血）mightseem simple. But recently, the British RED Cross asked parents with youngchildren how to help a child with a nosebleed. About 65 percent of parents didnot ____11____ the correct action to help.
2022年湖北省荆州市中考英语真题（解析版）
One night many yearsago, an angry voice woke me up from sleep. It was my drunken (喝醉的) father. Those days, he would always ___11___ home very late. Sometimes, he would also go on to fight with my mom.
2022年湖南省岳阳市中考英语真题（解析版）
FIFA World Cup is one of the biggest sportsevents in the world. It ___11___every 4 years. The first World Cup was in 1930. It has a history of over 90years. During the World Cup, ___12___fans watch the games and cheer for their favorite teams or players.
2022年湖北省荆州市中考英语真题（原卷版）
My earliest memory ofthese events began when I was around four years old. I was filled with ___12___ at that time. There were lots of ___13___ — crying, shouting, and doors slamming (砰地关上).
2022年湖北省武汉市中考英语真题（解析版）
The December day started like any other. Papacame back with his boat full of fish. Mama made breakfast for the family.Seven-year-old Joonas was doing his homework, while his two little brothers ranaround the yard. That day seemed peaceful, but Alejo ____16____ better.
2022年湖北省恩施州中考英语真题（解析版）
Once, herfather took her to the kitchen. He asked Jane to take a potato, an egg ____11____ two spoons of tea leaves. Jane was ____12____, andasked her father, “Do you want me to cook?”
2022年广西贵港市中考英语真题（原卷版）
Melatonin(褪黑素) is produced by the body to control when you get sleepy and whenyou wake up. As night falls, the levels of melatonin rise, telling the bodythat it’s time for bed. And the levels naturally fall as daylight comes near,getting you ready to greet the day.
