電大工程數(shù)學(xué)試卷及答案小抄參考

1、專業(yè)好文檔一、單項(xiàng)選擇題（每小題3分，共15分）在每小題列出的四個(gè)選項(xiàng)中只有一個(gè)是符合題目要求的，請(qǐng)將其代碼填在題后的括號(hào)內(nèi)。錯(cuò)選或未選均無分。得分評(píng)卷人1某人打靶3發(fā)，事件ai 表示“擊中i發(fā)”，i=0,1,2,3. 那么事件a=a1a2a3表示()。 a. 全部擊中. b. 至少有一發(fā)擊中. c. 必然擊中 d. 擊中3發(fā)2對(duì)于任意兩個(gè)隨機(jī)變量x和y，若e(xy)=e(x)e(y)，則有()。a. x和y獨(dú)立。 b. x和y不獨(dú)立。c. d(x+y)=d(x)+d(y) d. d(xy)=d(x)d(y)3下列各函數(shù)中可以作為某個(gè)隨機(jī)變量的概率密度函數(shù)的是（ ）。a 。 b. c. d.

2、，4設(shè)隨機(jī)變量x, y, , 則有（ ）a. 對(duì)于任意的, p1=p2 b. 對(duì)于任意的, p1 p25設(shè)x為隨機(jī)變量，其方差存在，c為任意非零常數(shù)，則下列等式中正確的是（） ad(x+c)=d(x). b. d(x+c)=d(x)+c. c. d(x-c)=d(x)-c d. d(cx)=cd(x)得分二、填空題（每空3分，共15分）評(píng)卷人6 設(shè)3階矩陣a的特征值為-1，1，2，它的伴隨矩陣記為a*， 則|a*+3a2e|= 。7設(shè)a= ，則= 。8設(shè)有3個(gè)元件并聯(lián)，已知每個(gè)元件正常工作的概率為p，則該系統(tǒng)正常工作的概率為 。9設(shè)隨機(jī)變量的概率密度函數(shù)為，則概率 。10設(shè)二維連續(xù)型隨機(jī)變量的

3、聯(lián)合概率密度函數(shù)為，則系數(shù) 。得分三、計(jì)算題（每小題10分，共50分）評(píng)卷人11求函數(shù)的傅氏變換 (這里)，并由此證明：12發(fā)報(bào)臺(tái)分別以概率0.6和0.4發(fā)出信號(hào)“1”和“0”。由于通訊系統(tǒng)受到干擾，當(dāng)發(fā)出信號(hào)“1”時(shí)，收?qǐng)?bào)臺(tái)未必收到信號(hào)“1”，而是分別以概率0.8和0.2收到信號(hào)“1”和“0”；同時(shí)，當(dāng)發(fā)出信號(hào)“0”時(shí)，收?qǐng)?bào)臺(tái)分別以概率0.9和0.1收到信號(hào)“0”和“1”。求（1）收?qǐng)?bào)臺(tái)收到信號(hào)“1”的概率；（2）當(dāng)收?qǐng)?bào)臺(tái)收到信號(hào)“1”時(shí)，發(fā)報(bào)臺(tái)確是發(fā)出信號(hào)“1”的概率。13設(shè)二維隨機(jī)變量的聯(lián)合概率函數(shù)是求：（1）常數(shù)c；（2）概率p(xy )；（3）x與y相互獨(dú)立嗎？請(qǐng)說出理由。14將n個(gè)

4、球隨機(jī)的放入n個(gè)盒子中去，設(shè)每個(gè)球放入各個(gè)盒子是等可能的，求有球盒子數(shù)x的數(shù)學(xué)期望。15設(shè)一口袋中依此標(biāo)有1，2，2，2，3，3數(shù)字的六個(gè)球。從中任取一球，記隨機(jī)變量x為取得的球上標(biāo)有的數(shù)字，求(1)x的概率分布律和分布函數(shù)。(2)ex得分四、證明題（共10分）評(píng)卷人16.設(shè)a=(a1,a2,an)t，a10,其長度為a，又a=aat,(1) 證明a2=a2a；(2) 證明a是a的一個(gè)特征向量，而0是a的n-1重特征值；(3) a能相似于對(duì)角陣嗎？若能,寫出對(duì)角陣.得分五、應(yīng)用題（共10分）評(píng)卷人17.設(shè)在國際市場上每年對(duì)我國某種出口商品的需求量x是隨機(jī)變量,它在2000,4000( 單位：噸

5、 )上服從均勻分布，又設(shè)每售出這種商品一噸，可為國家掙得外匯3萬元，但假如銷售不出而囤積在倉庫，則每噸需保養(yǎng)費(fèi)1萬元。問需要組織多少貨源，才能使國家收益最大。參考答案及評(píng)分標(biāo)準(zhǔn)一、 選擇題（每小題3分，共15分）1b2c3d4a5a 二、 填空題（每小題3分，共15分）6. 9 7. 1 8. 1(1p)3 9. 3/4 10. 12三、計(jì)算題（每題10分，共50分）11.解答：函數(shù)f(t)的付氏變換為：f(w)= （3分） = (2分)由付氏積分公式有f(t)=f(w)= (2分) = = （2分）所以 （1分）12.解答: 設(shè) a1=“發(fā)出信號(hào)1”，a0=“發(fā)出信號(hào)0”，a=“收到信號(hào)1”

6、 （2分）(1)由全概率公式 （1分）有 p(a)=p(a|a1)p(a1)+p(a|a0)p(a0) （2分） =0.8x0.6+0.1 x0.4=0.52 （1分）(2)由貝葉斯公式 （1分）有 p(a1|a)=p(a|a1)p(a1)/ p(a) （2分） =0.8x0.6/0.52=12/13 （1分）13.解答:(1) 由聯(lián)合概率密度的性質(zhì)有即 （2分）從而 c=8 （2分）(2) （2分）(3) 當(dāng)x0時(shí)， （2分）當(dāng)x=0時(shí), 同理有 （1分）因 故x與y相互獨(dú)立 （1分）14.解答：設(shè) i =1,2,n (2分)則 (1分)因 (2分) (2分)因而 (2分)所以 (2分)15

7、.解答：（1）隨機(jī)變量的取值為1，2，3。 （1分）依題意有： （3分）的分布函數(shù) （1分）由條件知：當(dāng)時(shí)， （1分） 當(dāng)時(shí)， （1分）當(dāng)時(shí)， （1分）當(dāng)時(shí)， （1分）（2）ex=1 x 1/6+2 x 3/6+3 x 2/6= 13/6 （1分）四、證明題（共10分）(1) a2=aataat=ata aat =a2a （2分）(2)因 aa= aat a=ataa= a2a （2分）故a是a的一個(gè)特征向量。又a對(duì)稱，故a必相似于對(duì)角陣 （1分）設(shè)a diag(1,2,n)=b, 其中1,2,n是a的特征值 (1分)因rank(a)=1, 所以 rank(b)=1 (1分)從而1,2,n中必

8、有n-1個(gè)為0, 即0是a的n-1重特征值 （1分）(3) a對(duì)稱，故a必相似于對(duì)角陣，=diag(a2, 0,0) (2分)五、應(yīng)用題（共10分）解答:設(shè)y為預(yù)備出口的該商品的數(shù)量，這個(gè)數(shù)量可只介于2000與4000之間，用z表示國家的收益（萬元）, （1分）則有 （4分）因 x服從r(2000,4000), 故有 (1分)所以 =( y2 7000y + 4106 ) /1000 (3分)求極值得 y=3500 (噸) (1分)if we dont do that it will go on and go on. we have to stop it; we need the courag

9、e to do it.his comments came hours after fifa vice-president jeffrey webb - also in london for the fas celebrations - said he wanted to meet ivory coast international toure to discuss his complaint.cska general director roman babaev says the matter has been exaggerated by the ivorian and the british

10、 media.blatter, 77, said: it has been decided by the fifa congress that it is a nonsense for racism to be dealt with with fines. you can always find money from somebody to pay them.it is a nonsense to have matches played without spectators because it is against the spirit of football and against the

11、 visiting team. it is all nonsense.we can do something better to fight racism and discrimination.this is one of the villains we have today in our game. but it is only with harsh sanctions that racism and discrimination can be washed out of football.the (lack of) air up there watch mcayman islands-ba

12、sed webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about

13、how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investig

14、ation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska.baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weathe

15、r plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our d

16、ay-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expec

17、t a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.below, the earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. st

18、ill, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. it will be like he is diving into the shallow end.skydiver preps for the big jumpwhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to earth. but this will not be enough to stop him completely.if he goes too fast or spins out of control, he has a stabilization parachute