1. How is Hunan cuisine somewhat different from Sichuan cuisine?The heat in Sichuan cuisine comes from chilies and Sichuan peppercorns. Human cuisine is often hotter and the heat comes from just chilies.2.What are the reasons why Hunan people like spicy food?Because they are a bold people. But many Chinese people think that hot food helps them overcome the effects of rainy or wet weather.3.Why do so many people love steamed fish head covered with chilies?People love it because the meat is quite tender and there are very few small bones.4.Why does Tingting recommend bridge tofu instead of dry pot duck with golden buns?Because bridge tofu has a lighter taste.5 .Why is red braised pork the most famous dish?Because Chairman Mao was from Hunan, and this was his favorite food.Step 5: Instruct students to make a short presentation to the class about your choice. Use the example and useful phrases below to help them.? In groups of three, discuss what types of restaurant you would like to take a foreign visitor to, and why. Then take turns role-playing taking your foreign guest to the restaurant you have chosen. One of you should act as the foreign guest, one as the Chinese host, and one as the waiter or waitress. You may start like this:? EXAMPLE? A: I really love spicy food, so what dish would you recommend?? B: I suggest Mapo tofu.? A: Really ? what's that?
This section guides students to pay attention to the typical context of vocabulary use, helps students accumulate vocabulary around the key vocabulary of this unit, and uses the learned words and word chunks in different contexts to deeply understand their meaning and usage, so as to achieve the purpose of review and consolidation.The teaching design activities aim to guide students to pay attention to the typical context in which the target vocabulary is used, as well as the common vocabulary used in collocation, so that students can complete the sentence with correct words. In terms of vocabulary learning strategies, this unit focuses on cultivating students' ability to pay attention to collocation of words and to use word blocks to express meaning.For vocabulary learning, it is not enough just to know the meaning of a single word, but the most important thing is to master the common collocations of words, namely word blocks.Teachers should timely guide students to summarize common vocabulary collocation, such as verb and noun collocation, verb and preposition collocation, preposition and noun collocation, and so on.1. Guide students to understand and consolidate the meaning and usage of the vocabulary in the context, 2. Guide the students to use the unit topic vocabulary in a richer context3. Let the students sort out and accumulate the accumulated vocabulary, establishes the semantic connection between the vocabulary,4. Enable students to understand and master the vocabulary more effectivelyGuiding the Ss to use unit topic words and the sentence patterns in a richer context.
The theme of the listening section is " talking about scenery and culture along a journey."The part is designed to further lead the students to understand Canadian natural geography and social environment, and integrated into the cultural contrast by mentioning the long train journey from Beijing to Moscow routes. On this basis, the part activates students related travel experience, lets the student serial dialogue, guides the student to explore further the pleasure and meaning of the long journey, and Chinese and foreign cultural comparison.The part also provides a framework for the continuation of the dialogue, which is designed to provide a framework for students to successfully complete their oral expressions, and to incorporate an important trading strategy to end the dialogue naturally.1. Help students to understand and master some common English idioms in the context, and experience the expression effect of English idioms.2. Guide the students to understand the identity of different people in the listening context, and finish the dialogue according to their own experience.3. Instruct the students to use appropriate language to express surprise and curiosity about space and place in the dialogue, and master the oral strategy of ending the dialogue naturally.1. Instruct students to grasp the key information and important details of the dialogue.2. Instruct students to conduct a similar talk on the relevant topic.
解析:因為減法和除法運(yùn)算中交換兩個數(shù)的位置對計算結(jié)果有影響,所以屬于組合的有2個.答案:B2.若A_n^2=3C_(n"-" 1)^2,則n的值為( )A.4 B.5 C.6 D.7 解析:因為A_n^2=3C_(n"-" 1)^2,所以n(n-1)=(3"(" n"-" 1")(" n"-" 2")" )/2,解得n=6.故選C.答案:C 3.若集合A={a1,a2,a3,a4,a5},則集合A的子集中含有4個元素的子集共有 個. 解析:滿足要求的子集中含有4個元素,由集合中元素的無序性,知其子集個數(shù)為C_5^4=5.答案:54.平面內(nèi)有12個點,其中有4個點共線,此外再無任何3點共線,以這些點為頂點,可得多少個不同的三角形?解:(方法一)我們把從共線的4個點中取點的多少作為分類的標(biāo)準(zhǔn):第1類,共線的4個點中有2個點作為三角形的頂點,共有C_4^2·C_8^1=48(個)不同的三角形;第2類,共線的4個點中有1個點作為三角形的頂點,共有C_4^1·C_8^2=112(個)不同的三角形;第3類,共線的4個點中沒有點作為三角形的頂點,共有C_8^3=56(個)不同的三角形.由分類加法計數(shù)原理,不同的三角形共有48+112+56=216(個).(方法二 間接法)C_12^3-C_4^3=220-4=216(個).
(一)、亞太經(jīng)濟(jì)合作組織的宗旨和作用1、亞太經(jīng)合組織簡介:(1)、地位——當(dāng)今世界最大的區(qū)域性經(jīng)濟(jì)合作組織(2)、性質(zhì)——是促進(jìn)亞太國家和地區(qū)經(jīng)濟(jì)合作、推動共同發(fā)展的主要機(jī)構(gòu)。亞太經(jīng)濟(jì)合作組織(APEC,簡稱亞太經(jīng)合組織),是當(dāng)今世界最大的區(qū)域性經(jīng)濟(jì)合作組織,是促進(jìn)亞太國家和地區(qū)經(jīng)濟(jì)合作、推動共同發(fā)展的主要機(jī)構(gòu)。相關(guān)鏈接:1989年11月,在澳大利亞的倡議下,澳大利亞、美國、加拿大、日本、韓國、新西蘭和東盟六國的外交與經(jīng)濟(jì)部長在澳大利亞首都堪培拉召開部長級會議,正式宣告亞太經(jīng)合組織成立。此后,該組織不斷擴(kuò)大,到2004年底共有21個成員,既有美國、日本等發(fā)達(dá)國家,也有中國、馬來西亞、墨西哥等發(fā)展中國家。亞太經(jīng)合組織的宗旨是:為本地區(qū)人民的共同利益而保持經(jīng)濟(jì)的增長與發(fā)展,促進(jìn)成員間經(jīng)濟(jì)的相互依存,加強(qiáng)開放的多邊貿(mào)易體制,減少區(qū)域貿(mào)易和投資壁壘。
由樣本相關(guān)系數(shù)??≈0.97,可以推斷脂肪含量和年齡這兩個變量正線性相關(guān),且相關(guān)程度很強(qiáng)。脂肪含量與年齡變化趨勢相同.歸納總結(jié)1.線性相關(guān)系數(shù)是從數(shù)值上來判斷變量間的線性相關(guān)程度,是定量的方法.與散點圖相比較,線性相關(guān)系數(shù)要精細(xì)得多,需要注意的是線性相關(guān)系數(shù)r的絕對值小,只是說明線性相關(guān)程度低,但不一定不相關(guān),可能是非線性相關(guān).2.利用相關(guān)系數(shù)r來檢驗線性相關(guān)顯著性水平時,通常與0.75作比較,若|r|>0.75,則線性相關(guān)較為顯著,否則不顯著.例2. 有人收集了某城市居民年收入(所有居民在一年內(nèi)收入的總和)與A商品銷售額的10年數(shù)據(jù),如表所示.畫出散點圖,判斷成對樣本數(shù)據(jù)是否線性相關(guān),并通過樣本相關(guān)系數(shù)推斷居民年收入與A商品銷售額的相關(guān)程度和變化趨勢的異同.
1.對稱性與首末兩端“等距離”的兩個二項式系數(shù)相等,即C_n^m=C_n^(n"-" m).2.增減性與最大值 當(dāng)k(n+1)/2時,C_n^k隨k的增加而減小.當(dāng)n是偶數(shù)時,中間的一項C_n^(n/2)取得最大值;當(dāng)n是奇數(shù)時,中間的兩項C_n^((n"-" 1)/2) 與C_n^((n+1)/2)相等,且同時取得最大值.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.各二項式系數(shù)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 的展開式的各二項式系數(shù)之和為2^n1. 在(a+b)8的展開式中,二項式系數(shù)最大的項為 ,在(a+b)9的展開式中,二項式系數(shù)最大的項為 . 解析:因為(a+b)8的展開式中有9項,所以中間一項的二項式系數(shù)最大,該項為C_8^4a4b4=70a4b4.因為(a+b)9的展開式中有10項,所以中間兩項的二項式系數(shù)最大,這兩項分別為C_9^4a5b4=126a5b4,C_9^5a4b5=126a4b5.答案:1.70a4b4 126a5b4與126a4b5 2. A=C_n^0+C_n^2+C_n^4+…與B=C_n^1+C_n^3+C_n^5+…的大小關(guān)系是( )A.A>B B.A=B C.A<B D.不確定 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
Step 7: complete the discourse according to the grammar rules.Cholera used to be one of the most 1.__________ (fear) diseases in the world. In the early 19th century, _2_________ an outbreak of cholera hit Europe, millions of people died. But neither its cause, 3__________ its cure was understood. A British doctor, John Snow, wanted to solve the problem and he knew that cholera would not be controlled _4_________ its cause was found. In general, there were two contradictory theories 5 __________ explained how cholera spread. The first suggested that bad air caused the disease. The second was that cholera was caused by an _6_________(infect) from germs in food or water. John Snow thought that the second theory was correct but he needed proof. So when another outbreak of cholera hit London in 1854, he began to investigate. Later, with all the evidence he _7_________ (gather), John Snow was able to announce that the pump water carried cholera germs. Therefore, he had the handle of the pump _8_________ (remove) so that it couldn't be used. Through his intervention,the disease was stopped in its tracks. What is more, John Snow found that some companies sold water from the River Thames that __9__________________ (pollute) by raw waste. The people who drank this water were much more likely _10_________ (get) cholera than those who drank pure or boiled water. Through John Snow's efforts, the _11_________ (threaten) of cholera around the world saw a substantial increase. Keys: 1.feared 2.when 3. nor 4.unless 5.that/which 6.infection 7.had gathered 8.removed 9.was polluted 10.to get 11. threat
Step 5: After learning the text, discuss with your peers about the following questions:1.John Snow believed Idea 2 was right. How did he finally prove it?2. Do you think John Snow would have solved this problem without the map?3. Cholera is a 19th century disease. What disease do you think is similar to cholera today?SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.keys:1. John Snow finally proved his idea because he found an outbreak that was clearly related to cholera, collected information and was able to tie cases outside the area to the polluted water.2. No. The map helped John Snow organize his ideas. He was able to identify those households that had had many deaths and check their water-drinking habits. He identified those houses that had had no deaths and surveyed their drinking habits. The evidence clearly pointed to the polluted water being the cause.3. SARS and Covid-19 because they are both deadly and fatally infectious, have an unknown cause and need serious public health care to solve them urgently.Step 6: Consolidate what you have learned by filling in the blanks:John Snow was a well-known _1___ in London in the _2__ century. He wanted to find the _3_____ of cholera in order to help people ___4_____ it. In 1854 when a cholera __5__ London, he began to gather information. He ___6__ on a map ___7___ all the dead people had lived and he found that many people who had ___8____ (drink) the dirty water from the __9____ died. So he decided that the polluted water ___10____ cholera. He suggested that the ___11__ of all water supplies should be _12______ and new methods of dealing with ____13___ water be found. Finally, “King Cholera” was __14_____.Keys: 1. doctor 2. 19th 3.cause 4.infected with 5.hit 6.marked 7.where 8.drunk 9.pump 10.carried 11.source 12.examined 13.polluted 14.defeatedHomework: Retell the text after class and preview its language points
This happens because the dish soap molecules have a strong negative charge, and the milk molecules have a strong positive charge. Like magnets, these molecules are attracted to each other, and so they appear to move around on the plate, taking the food coloring with them, making it look like the colors are quickly moving to escape from the soap.Listening text:? Judy: Oh, I'm so sorry that you were ill and couldn't come with us on our field trip. How are you feeling now? Better?? Bill: Much better, thanks. But how was it?? Judy: Wonderful! I especially liked an area of the museum called Light Games.it was really cool. They had a hall of mirrors where I could see myself reflected thousands of times!? Bill: A hall of mirrors can be a lot of fun. What else did they have?? Judy: Well, they had an experiment where we looked at a blue screen for a while, and then suddenly we could see tiny bright lights moving around on it. You'll never guess what those bright lights were!? Bill: Come on, tell me!? Judy: They were our own blood cells. For some reason, our eyes play tricks on us when we look at a blue screen, and we can see our own blood cells moving around like little lights! But there was another thing I liked better. I stood in front of a white light, and it cast different shadows of me in every color of the rainbow!? Bill: Oh, I wish I had been there. Tell me more!? Judy: Well, they had another area for sound. They had a giant piano keyboard that you could use your feet to play. But then, instead of playing the sounds of a piano, it played the voices of classical singers! Then they had a giant dish, and when you spoke into it, it reflected the sound back and made it louder. You could use it to speak in a whisper to someone 17 meters away.? Bill: It all sounds so cool. I wish I could have gone with you? Judy: I know, but we can go together this weekend. I'd love to go there again!? Bill: That sounds like a great idea!
The grammatical structure of this unit is predicative clause. Like object clause and subject clause, predicative clause is one of Nominal Clauses. The leading words of predicative clauses are that, what, how, what, where, as if, because, etc.The design of teaching activities aims to guide students to perceive the structural features of predicative clauses and think about their ideographic functions. Beyond that, students should be guided to use this grammar in the context apporpriately and flexibly.1. Enable the Ss to master the usage of the predicative clauses in this unit.2. Enable the Ss to use the predicative patterns flexibly.3. Train the Ss to apply some skills by doing the relevant exercises.1.Guide students to perceive the structural features of predicative clauses and think about their ideographic functions.2.Strengthen students' ability of using predicative clauses in context, but also cultivate their ability of text analysis and logical reasoning competence.Step1: Underline all the examples in the reading passage, where noun clauses are used as the predicative. Then state their meaning and functions.1) One theory was that bad air caused the disease.2) Another theory was that cholera was caused by an infection from germs in food or water.3) The truth was that the water from the Broad Street had been infected by waste.Sum up the rules of grammar:1. 以上黑體部分在句中作表語。2. 句1、2、3中的that在從句中不作成分,只起連接作用。 Step2: Review the basic components of predicative clauses1.Definition
4.寫出下列隨機(jī)變量可能取的值,并說明隨機(jī)變量所取的值表示的隨機(jī)試驗的結(jié)果.(1)一個袋中裝有8個紅球,3個白球,從中任取5個球,其中所含白球的個數(shù)為X.(2)一個袋中有5個同樣大小的黑球,編號為1,2,3,4,5,從中任取3個球,取出的球的最大號碼記為X.(3). 在本例(1)條件下,規(guī)定取出一個紅球贏2元,而每取出一個白球輸1元,以ξ表示贏得的錢數(shù),結(jié)果如何?[解] (1)X可取0,1,2,3.X=0表示取5個球全是紅球;X=1表示取1個白球,4個紅球;X=2表示取2個白球,3個紅球;X=3表示取3個白球,2個紅球.(2)X可取3,4,5.X=3表示取出的球編號為1,2,3;X=4表示取出的球編號為1,2,4;1,3,4或2,3,4.X=5表示取出的球編號為1,2,5;1,3,5;1,4,5;2,3,5;2,4,5或3,4,5.(3) ξ=10表示取5個球全是紅球;ξ=7表示取1個白球,4個紅球;ξ=4表示取2個白球,3個紅球;ξ=1表示取3個白球,2個紅球.
(一)持續(xù)扮靚城市顏值。深入實施精細(xì)化保潔,高效完成所轄476萬平方米的高架橋、隧道的保潔任務(wù)和196萬平方米的城市家具一體化保潔的監(jiān)管任務(wù),落實“九機(jī)九步”作業(yè)法,先后完成應(yīng)急保障任務(wù)約110余次。全面整治市容秩序,深入開展臨街建筑外立面管理,已對臨街建筑外立面維護(hù)、出新2306處、面積約5.6萬平方米,清理非法小廣告及亂貼亂畫10.8萬處,清理亂堆亂放3.1萬余處。持續(xù)推進(jìn)基礎(chǔ)設(shè)施建設(shè)。積極推進(jìn)****生活垃圾綜合轉(zhuǎn)運(yùn)中心項目、市中區(qū)生活固廢液綜合轉(zhuǎn)運(yùn)項目、****生活垃圾分類處置中心等大型示范項目。利用廢棄礦坑回填、山體修復(fù)、土地復(fù)耕、園林綠化、樓槽回填等項目與工程渣土直接利用相結(jié)合,設(shè)立建筑渣土直接利用點319個,庫容量約3376萬噸,目前全市正在運(yùn)行的資源化利用企業(yè)5家,年處理能力785萬噸。
The newspaper reported more than 100 people had been killed in the thunderstorm.報紙報道說有一百多人在暴風(fēng)雨中喪生。(2)before、when、by the time、until、after、once等引導(dǎo)的時間狀語從句的謂語是一般過去時,以及by、before后面接過去的時間時,主句動作發(fā)生在從句的動作或過去的時間之前且表示被動時,要用過去完成時的被動語態(tài)。By the time my brother was 10, he had been sent to Italy.我弟弟10歲前就已經(jīng)被送到意大利了。Tons of rice had been produced by the end of last month. 到上月底已生產(chǎn)了好幾噸大米。(3) It was the first/second/last ... time that ...句中that引導(dǎo)的定語從句中,主語與謂語構(gòu)成被動關(guān)系時,要用過去完成時的被動語態(tài)。It was the first time that I had seen the night fact to face in one and a half years. 這是我一年半以來第一次親眼目睹夜晚的景色。(4)在虛擬語氣中,條件句表示與過去事實相反,且主語與謂語構(gòu)成被動關(guān)系時,要用過去完成時的被動語態(tài)。If I had been instructed by him earlier, I would have finished the task.如果我早一點得到他的指示,我早就完成這項任務(wù)了。If I had hurried, I wouldn't have missed the train.如果我快點的話,我就不會誤了火車。If you had been at the party, you would have met him. 如果你去了晚會,你就會見到他的。
The discourse explores the link between food and culture from a foreign’s perspective and it records some authentic Chinese food and illustrates the cultural meaning, gerography features and historic tradition that the food reflects. It is aimed to lead students to understand and think about the connection between food and culture. While teaching, the teacher should instruct students to find out the writing order and the writer’s experieces and feelings towards Chinese food and culture.1.Guide the students to read the text, sort out the information and dig out the topic.2.Understand the cultural connotation, regional characteristics and historical tradition of Chinese cuisine3.Understand and explore the relationship between food and people's personality4.Guide the students to use the cohesive words in the text5.Lead students to accurately grasp the real meaning of the information and improve the overall understanding ability by understanding the implied meaning behind the text.1. Enable the Ss to understand the structure and the writing style of the passage well.2. Lead the Ss to understand and think further about the connection between food and geography and local character traits.Step1: Prediction before reading. Before you read, look at the title, and the picture. What do you think this article is about?keys:It is about various culture and cuisine about a place or some countries.
You have no excuse for not going.你沒有理由不去。He was punished for not having finished his homework.他因未完成作業(yè)而受到懲罰。2.動詞ing形式復(fù)合結(jié)構(gòu)由物主代詞或人稱代詞賓格、名詞所有格或普通格加動詞ing,即“sb./sb.'s+doing”構(gòu)成。動詞ing形式的復(fù)合結(jié)構(gòu)實際上是給動詞ing形式加了一個邏輯主語。動詞ing形式的復(fù)合結(jié)構(gòu)有四種形式:①形容詞性物主代詞+動詞ing②名詞所有格+動詞ing③代詞賓格+動詞ing④名詞+動詞ingHer coming to help encouraged all of us.她來幫忙鼓舞了我們所有人。The baby was made awake by the door suddenly shutting.這個嬰兒被突然的關(guān)門聲吵醒了。Can you imagine him/Jack cooking at home?你能想象他/杰克在家做飯的樣子嗎?無生命名詞無論是作主語還是作賓語都不能用第②種形式。Tom's winning first prize last year impressed me a lot.湯姆去年得了一等獎使我印象深刻。Do you mind my/me/Jack's/Jack leaving now?你介意我/杰克現(xiàn)在離開嗎?Excuse me for my not coming on time.很抱歉我沒能按時來。His father's being ill made him worried.他父親病了,他很擔(dān)心。We are looking forward to the singer's/the singer to give us a concert.我們盼望著這位歌手來給我們舉辦一場演唱會。
當(dāng)孩子們由父母陪同時,他們才被允許進(jìn)入這個運(yùn)動場。3.過去分詞(短語)作狀語時的幾種特殊情況(1)過去分詞(短語)在句中作時間、條件、原因、讓步狀語時,相當(dāng)于對應(yīng)的時間、條件、原因及讓步狀語從句。Seen from the top of the mountain (=When it is seen from the top of the mountain), the whole town looks more beautiful.從山頂上看,整個城市看起來更美了。Given ten more minutes (=If we are given ten more minutes), we will finish the work perfectly.如果多給十分鐘,我們會完美地完成這項工作。Greatly touched by his words (=Because she was greatly touched by his words), she was full of tears.由于被他的話深深地感動,她滿眼淚花。Warned of the storm (=Though they were warned of the storm), the farmers were still working on the farm.盡管被警告了風(fēng)暴的到來,但農(nóng)民們?nèi)栽谵r(nóng)場干活。(2)過去分詞(短語)在句中作伴隨、方式等狀語時,可改為句子的并列謂語或改為并列分句。The teacher came into the room, followed by two students (=and was followed by two students).后面跟著兩個學(xué)生,老師走進(jìn)了房間。He spent the whole afternoon, accompanied by his mom(=and was accompanied by his mom).他由母親陪著度過了一整個下午。
The grammar of this unit is designed to review noun clauses. Sentences that use nouns in a sentence are called noun clauses. Nominal clauses can act as subject, object, predicate, appositive and other components in compound sentences. According to the above-mentioned different grammatical functions, nominal clauses are divided into subject clause, object clause, predicate clause and appositive clause. In this unit, we will review the three kinds of nominal clauses. Appositive clauses are not required to be mastered in the optional compulsory stage, so they are not involved.1. Guide the students to judge the compound sentences and determine the composition of the clauses in the sentence.2. Instruct students to try to learn grammar by generalizing grammar rules, controlling written practice, and semi-open oral output.3. Inspire the students to systematize the function and usage of noun clause1.Instruct students to try to learn grammar by generalizing grammar rules, controlling written practice, and semi-open oral output.2.Inspire the students to systematize the function and usage of noun clauseStep1: The teacher ask studetns to find out more nominal clauses from the reading passage and udnerline the nominal clauses.
3.下結(jié)論.依據(jù)均值和方差做出結(jié)論.跟蹤訓(xùn)練2. A、B兩個投資項目的利潤率分別為隨機(jī)變量X1和X2,根據(jù)市場分析, X1和X2的分布列分別為X1 2% 8% 12% X2 5% 10%P 0.2 0.5 0.3 P 0.8 0.2求:(1)在A、B兩個項目上各投資100萬元, Y1和Y2分別表示投資項目A和B所獲得的利潤,求方差D(Y1)和D(Y2);(2)根據(jù)得到的結(jié)論,對于投資者有什么建議? 解:(1)題目可知,投資項目A和B所獲得的利潤Y1和Y2的分布列為: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 ,說明投資A項目比投資B項目期望收益要高;同時 ,說明投資A項目比投資B項目的實際收益相對于期望收益的平均波動要更大.因此,對于追求穩(wěn)定的投資者,投資B項目更合適;而對于更看重利潤并且愿意為了高利潤承擔(dān)風(fēng)險的投資者,投資A項目更合適.
對于離散型隨機(jī)變量,可以由它的概率分布列確定與該隨機(jī)變量相關(guān)事件的概率。但在實際問題中,有時我們更感興趣的是隨機(jī)變量的某些數(shù)字特征。例如,要了解某班同學(xué)在一次數(shù)學(xué)測驗中的總體水平,很重要的是看平均分;要了解某班同學(xué)數(shù)學(xué)成績是否“兩極分化”則需要考察這個班數(shù)學(xué)成績的方差。我們還常常希望直接通過數(shù)字來反映隨機(jī)變量的某個方面的特征,最常用的有期望與方差.二、 探究新知探究1.甲乙兩名射箭運(yùn)動員射中目標(biāo)靶的環(huán)數(shù)的分布列如下表所示:如何比較他們射箭水平的高低呢?環(huán)數(shù)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類似兩組數(shù)據(jù)的比較,首先比較擊中的平均環(huán)數(shù),如果平均環(huán)數(shù)相等,再看穩(wěn)定性.假設(shè)甲射箭n次,射中7環(huán)、8環(huán)、9環(huán)和10環(huán)的頻率分別為:甲n次射箭射中的平均環(huán)數(shù)當(dāng)n足夠大時,頻率穩(wěn)定于概率,所以x穩(wěn)定于7×0.1+8×0.2+9×0.3+10×0.4=9.即甲射中平均環(huán)數(shù)的穩(wěn)定值(理論平均值)為9,這個平均值的大小可以反映甲運(yùn)動員的射箭水平.同理,乙射中環(huán)數(shù)的平均值為7×0.15+8×0.25+9×0.4+10×0.2=8.65.